SAMPLE SHEET: GATE 2015; THERMODYNAMICS (MECHANICAL ENGINEERING)

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PRACTICE WORKSHEET GATE-2015

MECHANICAL ENGINEERING

TOPIC: BASIC THERMODYNAMICS

Difficulty Level: 1

SET ONE: Each question has several entries, choose the most appropriate one

01) Gas laws are applicable to

            a) Gases as well as vapours     b) Gases alone and not applicable to vapours

            c) Gases and Steam                  d) Gases and Superheated vapours

02) An ideal gas compared to a real gas at very high pressures occupies

            a) more volume           b) less volume            

c) same volume           d) can’t be predicted

03) Temperature of a gas is produced due to

            a) its heating value                   b) kinetic energy of the molecules

            c) molecular vibration              d) inter-molecular attractions

04)  According to kinetic theory of gases, the absolute zero temperature is attained when

            a) volume of the gas is zero                             b) pressure of the gas is zero

            c) kinetic energy of the molecule is zero                     d)  specific heat is zero 

05)  The quantity δQ – δW; where δQ is elemental heat transfer and δW is the elemental work    

transfer is

            a) path function                       b) point function

            c) cyclic function                     d) in-exact differential

06)  The workdone in an adiabatic process between a given pair of end states depends on

            a) the values of the endstates only,      b) the end states and specific heat ratio  γ

            c) the end states and polytropic index n,          d) none of the above.

07)  If the value of polytropic index n is high, then the compressor work between given pressure limits will be

            a) less                                      b) more

            c) no effect                              d) zero

08)  A perfect gas at 27^oC is heated at constant pressure till its volume becomes double. The final temperature will be

            a) 54^oC                                    b) 327^oC

            c) 108^oC                                  d) 600^oC

09)  Mixing of ice and water at 0^oC at atmospheric pressure is an example of

            a) reversible process                b) irreversible process

            c) quasi-static process              d) isentropic process

10)  Change in enthalpy in a closed system is equal to heat transferred if the reversible process takes place at constant

            a) pressure                               b) temperature

            c) volume                                d) entropy

ME-301: THERMODYNAMICS FOR THIRD SEMESTER; UPTU

SECTION A: Each question carry 2 marks

01) What is point function and path function?

02) Define Enthalpy.

03) What is SFEE?

04) What is internal energy of a system

05) What is vapour dome and dryness factor?

06) What is saturated liquid line and saturated vapour line?

07) What is triple point of water?

08) Define specific heats of ideal gases.

09) Write the reduced form of Vander Waals equation for real gases.

10) Define a thermodynamic system.

11) State with reasoning whether the following systems are closed, open or isolated
i) Refrigerator; ii) Pressure Cooker

12) Distinguish between isolated system and adiabatic system.

13) Explain the concept of flow work

14) What is control volume and control surface?

15) When does a real gas behave like an ideal gas?

16) What are extensive and intensive properties?

17) What is enthalpy of evaporation of steam?

18) Define degree of under-cooling and degree of superheat.

19) What is COP of a heat pump?

20) Define throttling process.

21) Define entropy.

22) Two moles of an ideal gas occupy a volume of 4.24 m³ at 400 K temperature. Find the pressure exerted by the gas.

23) Distinguish between refrigerator and heat pump.

24) What is Free Expansion?

25) Explain Zeroth law of thermodynamics.

26) Explain the concept of compressibility factor?

27) What is PMM-1.

28) What is a superheated steam?

29) Distinguish between universal gas constant and characteristic gas constant.

30) What is Exergy?

31) Distinguish between quasi-static process and reversible process.

32) What is a diathermal system boundary?

33) What is a steady flow open system?

34) What is the difference between latent heat and sensible heat?

35) What is a thermodynamic cycle?

36) Distinguish between restraint and unrestraint process.

37) What is a thermodynamic definition of work?

38) What is work of evaporation?

39) What is a pure substance?

40) What is the concept of continuum?

41) Define thermodynamic state, process and path.

42) Distinguish between thermal equilibrium and thermodynamic equilibrium.

43) What are the conditions for reversible process?

44) Distinguish between heat and work.

45) What are the differences between gas and vapour?

SECTION B: Attempt any three of the following questions. Each question contains two parts of 5 marks each. Total marks In this section is 3x10 = 30

01) a) State Zeroth law of thermodynamics and explain how it leads to the concept of temperature.

b) Explain different types of temperature scale and the relations among them.

02) a) Explain the corollaries of first law of thermodynamics.

b) 2 kg of air is confined in a rigid container of 0.42 m³ at 4 bar pressure. When heat energy of 164 kJ is added, its temperature becomes 127°C.
Find :

i) Work done by the system.
ii) Change in internal energy.
iii) Specific heat at constant volume.

03) a) Derive an expression for heat transfer and work done in a polytropic process.

b) 1.5 kg of oxygen contained in a cylinder at 4 bar pressure and 300 K expands three times its original volume in a constant pressure process. Determine
i) Initial volume, ii) Final temperature, iii) Work done by the gas, iv) Heat added and v) Change in internal energy.
; Assume C_p = 1.005 kJ/kg-K and R = 260 J/kg-K

04) a) Make steady flow energy analysis on a turbine.

b) Find the velocity and diameter at exit of a nozzle if 5 kg/s air at 9 bar and 200°C expands through the nozzle up to pressure at 1.1 bar. Approach velocity is 50 m/s.

05) a) Differentiate between absolute pressure and gauge pressure. What is a manometer?

b) An ideal gas of molecular weight 42.4 has a pressure of 10 bar and occupies a volume of 0.3 m³ at 27°C. Determine the characteristic gas constant for the ideal gas, its mass and number of moles.

06) a) Write the first law of thermodynamics for a flow process. Derive an expression for flow work.

b) Find the total work done and efficiency for a reversible Carnot cycle.

07) a) What is continuity equation in flow process?

b) 3 kg air at 2 bar pressure and 27℃ temperature has been compressed isothermally till the pressure reaches 6 bar. Next it has been heated at constant pressure and thereafter reaches the initial state by expanding adiabatically. Find the maximum Temperature reached in the cycle and total work done by the system.

08) a) Explain the Joule's experiment.

b) Prove that internal energy is a point function.

09) a) What is thermodynamic temperature scale?

b) i) A heat engine running between 300 K and 800 K generates 2000 kJ of energy. Find the total heat extracted from the source.
ii) Determine the power required to run a refrigerator that transfers 2000 kJ/min of heat from a cooled space at 0°C to the surroundings atmosphere at 27°C.

10) a) What is PMM - 2? State Kelvin-Planck statement of second law of thermodynics.

b) A heat engine running between two thermal reservoirs of 800 K and 300 K is used to power a refrigerator running between two thermal reservoirs of 325 K and 260 K. If the heat engine draws 5000 kJ heat from reservoirs at 800 K, then find the amount of heat extracted from 260 K reservoir by the refrigerator.

11) a) Explain the Vander Waal's gas equation.

b) 4 kg of steam at 16 bar occupies a volume of 0.28 m³. The steam expands at constant volume to a pressure of 8 bar. Determine the final dryness fraction, final internal energy and change in entropy.

12) a) Explain and derive Clausius Inequality.

b) 3 kg of air is heated reversibly at constant pressure of 2.5 bar from 23°C to 227°C. If the lowest available temperature is 20°C determine the increase in the available energy of air due to heating. Take C_p = 1.005 kJ/kg-K.

13) a) What is thermodynamic definitions of work? Distinguish between ∫pdV work and other types of work.

b) 3 kg of air at 1.5 bar pressure and 350 K is compressed isothermally to a pressure of 6 bar. Then heat of 350 kJ is added at constant volume. What will be the maximum temperature of air during the process? Find the total work done in the processes. Also find the change in internal energy of air.

14) a) Write the limitations of second law of thermodynamics. Prove that C_p - C_v = R

b) 10 kg of air at 300 K is stored in a totally insulated cylinder of volume 0.3 m³/kg. If 1 kg air has been taken out of the system, then what will be the value of new pressure?

15) a) Steam at 1.2 bar and a dryness fraction of 0.5 is heated at constant pressure until it becomes saturated vapour. Calculate the heat transferred per kg of steam.

b) Steam at 8 MPa and 500°C passes through a throttling process such that the pressure is suddenly dropped to 0.3 MPa. Find the expected temperature after throttling.

16) a) What are the causes of irreversibility?

b) Distinguish between a quasi-static process and reversible process.

17) a) 3 kg of air at 400 K and 4 bar pressure adiabatically mixed with 4 kg of air at 500 K and 3 bar pressure. Find the change in entropy of the universe.

b) Explain the principle of increase of entropy.

SECTION C : marks 50, 5 questions of 10 mark each. Each question contains 3 parts. Attempt any two parts out of three from each question.

01) a) Steam at 20 bar pressure and 300°C expands isentropically in a turbine to a pressure of 2 bar. Find the final condition of the steam. Also Calculate the work delivered by the turbine.

b) What is isentropic efficiency of a turbine? Calculate internal energy of steam at 6 bar pressure and 300°C.

c) Explain the steam formation process at constant pressure.

02) a) What is adiabatic mixing of two ideal gases? Derive the expressions for final temperature and pressure.

b) 5 kg of steam at 8 bar pressure and 200°C mixed with 3 kg of steam at 5 bar and dryness fraction x = 0.8 adiabatically. Find the final condition of the steam.

c) 5 kg of air at 4 bar pressure is heated at constant pressure from 300 K to 500 K. Find the change in entropy of the system.

03) a) Prove that in an adiabatic process pV^γ = Constant.

b) Polytropic compression of air from state 1 to state 2 where p₁ = 100 kPa and T₁ = 300 K, p₂ = 300 kPa and n = 1.2 where as mass of air is 3 kg. If R = 0.287 kJ/kg-K. Then find

i) heat exchange during the process
ii) change in internal energy
iii) total work done by the air
iv) change in entropy


c) A non flow reversible process occurs for which pressure and volume are correlated by the relation p = (V² + 6V), where V is the volume in m³ and pressure p is in bar. Determine work done if volume changes from 3 to 6 m³.

04) a) A gas expands according to the equation pv = 100, where " p " is the pressure in kPa and " v " is the specific volume. Initial and final pressures are 1000 kPa and 500 kPa respectively. The gas is then heated at constant volume back to it'd original pressure of 1000 kPa. Determine the net work done. Also sketch the processes in p-v coordinates.

b) What is the definition of thermodynamic work?

c) What is the efficiency of a thermodynamic cycle?

05) a) What is paddle work? Distinguish between ∫pdV work and ∫-vdp work.

b) If pV = mRT, determine whether the expression (V/T).dp + (p/T).dV is a property of a system.

c) 2 kg of air at 1 bar pressure and 300 K is compressed adiabatically to a pressure of 6 bar. Then heat of 200 kJ is added at constant pressure. What will be the maximum temperature of air during the process? Find the total work done in the processes. Also find the change in internal energy of air.

06) a) Find the expression for heat transfer in terms of work done in a polytropic process.

b) What is the specific heat C_n for a polytropic process?

c) 2 kg of air at pressure 2 bar and 300 K is compressed reversibly to 4 bar and 650 K temperature in a polytropic process. Determine the polytropic index (n) of the process.

07) a) Find an expression for mechanical work in steady flow process.

b) What is the meaning of - vdp work?

c) Air flows through a gas turbine system at a rate of 5 kg/s. It enters with a velocity of 150 m/s and an enthalpy of 1000 kJ/kg. At exit the velocity is 120 m/s and enthalpy is 600 kJ/kg. If the air passing through the turbine looses 30 kJ/kg of heat to the surroundings, determine the power developed by the system.

08) a) Write the assumptions considered in Kinetic theory of gases? Prove that C_p - C_v = R

b) Explain the law of corresponding states.

c) 10 kg of air at 300 K is stored in a cylinder of volume 0.3 m³/kg. Find the pressure exerted by air using Vander Waals gas equation. Critical properties of air are: P_c = 37.7 bar, T_c = 132.5 K, v_c = 0.093 m³/kg_mole, R = 287 J/kg-K

09) a) What are the limitations of Vander Waals gas equation? Explain reduced properties of a real gas?

b) What is a undercooled liquid and degree of undercooling? Also define enthalpy of water.

c) What are the properties of steam at critical state? Explain sublimation process and triple point line.

10) a) What are the differences between dry saturated steam and superheated steam at a same pressure? Also, explain vapourdome, saturated liquid line, saturated vapour line and critical point.

b) What are the differences between work of evaporation and enthalpy of evaporation?

c) An inventor claims to have developed a refrigeration unit which maintains −10℃ in the refrigerator which is kept at a room where the surrounding temperature is 25℃ and which has COP of 8.5. Find the claim of the inventor is possible or not.

11) a) Prove that the absolute zero temperature is impossible to achieve according to second law of thermodynamics.

b) Two reversible heat engines A and B are arranged in series. A rejects heat directly to B. Engine A receives 200 kJ at a temperature of 421℃ from the hot source while engine B is in communication with a cold sink at a temperature of 5℃. If work output of A is twice that of B, find :
(i) Intermediate temperature between A and B.
(ii) Efficiency of each engine.
(iii) Heat rejected to the sink.


c) Prove that the reversible heat engines are the most efficient.

12) a) Steam at 1 bar and a dryness fraction of 0.523 is heated in a rigid vessel until it becomes saturated vapour. Calculate the heat transferred per kg of steam.

b) Steam at 9 MPa and 600°C passes through a throttling process such that the pressure is suddenly dropped to 0.4 MPa. Find the expected temperature after throttling.

c) What will be the quality of the steam at the end of adiabatic expansion of steam at 12 bar pressure and 400°C to 1.2 bar in a turbine. Also, find the ideal work out put by the turbine.

13) a) Explain the change of entropy in a perfectly isolated system during a process in the system.

b) Explain the conditions those must be satisfied by a reversible process.

c) Two kg of water at 90℃ is mixed with three kg of water at 10℃ in a perfectly isolated system. Calculate the change in entropy of the system.

14) a) Explain the second law of thermodynamics and prove that no engine can have a 100% efficiency.

b) Explain the theoretical Carnot cycle and derive its efficiency with diagrams.

c) A reversible engine working in a cycle takes 4800 kJ of heat per minute from a source at 800 K and develops 35 kW power. The engine rejects heat to two reservoirs at 300 K and 360 K. Determine the heat rejected to each sink.

15) a) What are the causes of external irreversibility?

b) Write the first and second Tds equations and derive the expression for the change of entropy during a polytropic process.

c) Prove that reversible engines are most efficient.

16) a) Explain the second law of thermodynamics.

b) Derive the Clausius inequality.

c) Steam at 160 bar and 550℃ is supplied to a steam turbine. The expansion of steam is adiabatic with increase in entropy of 0.1 kJ/kg-K. If the exhaust pressure is 0.2 bar, calculate specific work of expansion.

17) a) 5 kg of water at 400 K is isobarically and adiabatically mixed with 3 kg of water at 500 K. Find the change in entropy of the universe.

b) Explain i) Second law efficiency, ii) Effectiveness of a system and iii) Availability of a closed system.

c) Explain the principle of increase of entropy.

18) a) Explain Helmholtz and Gibbs function.

b) Explain the concept of PMM-I and PMM-II.

c) Find an expression of exit velocity C₂ in terms of pressure ratio when air passes through a nozzle from a pressure of p₁ and temperature T₁ to a pressure p₂.

19) a) Distinguish between enthalpy and internal energy.

b) What is absolute or thermodynamic temperature? Explain briefly.

c) Two Carnot engines work in series between the source at temperature 500 K and sink at temperature 300 K. If both develop equal power, determine the intermediate temperature.

20) a) Show that two adiabatic curves on p-V diagram never intersects each other.

b) Define and classify thermodynamic systems.

c) In an isentropic flow through nozzle, air flows at the rate of 600 kg/hr. At inlet to the nozzle pressure is 2 MPa and temperature is 27℃. The exit pressure is 0.5 MPa. Initial air velocity is 300 m/s, determine
i) exit velocity of air
ii) inlet and exit area of the nozzle

THE END

THERMODYNAMICS: BASIC CONCEPTS AND DEFINITIONS

UNIT- I:

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Fundamental Concepts and Definitions; Terminology, Definition and Scope; Microscopic and Macroscopic Approaches; Engineering Thermodynamics; it's definition and practical applications; Systems and Control volumes; Characteristics of System boundary and Control Surfaces; Surroundings and fixed, moving and imaginary boundaries; Thermodynamic States, state point; identification of a state through properties; definitions and units; extensive, intensive and specific properties, Thermodynamic planes and coordinate systems using properties; Change of state, path and processes; Quasi-static processes; Reversible processes, Restrained and unrestrained processes; Thermodynamic Equilibrium; diathermic wall, Zeroth Law of thermodynamics, Temperature as an important properties.

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Q.1) What is the meaning of Thermodynamics?

Ans:) The branch of science that deals with energy and its movements in the space is generally known as Thermodynamics. The study of this science is based upon experimental values and common experiences and the laws are empirical in thermodynamics.

¤ Introduction:

The most of general sense of thermodynamics is the study of energy and its relationship to the properties of matter. All activities in nature involve some interaction between energy and matter. Thermodynamics is a science that governs the following:

• (i) Energy and its transformation
• (ii) Feasibility of a process involving transformation of energy
• (iii) Feasibility of a process involving transfer of energy
• (iv) Equilibrium processes

More specifically, thermodynamics deals with energy conversion, energy exchange and the direction of exchange.

¤ Areas of Application of Thermodynamics:

All natural processes are governed by the principles of thermodynamics. However, the following engineering devices are typically designed based on the principles of thermodynamics.

Automotive engines, Turbines, Compressors, Pumps, Fossil and Nuclear Power Plants, Propulsion systems for the Aircrafts, Separation and Liquefaction Plant, Refrigeration, Air-conditioning and Heating Devices.

The principles of thermodynamics are summarized in the form of a set of axioms. These axioms are known as four thermodynamic laws:

• Zeroth law of thermodynamics,
• First law of thermodynamics,
• Second law of thermodynamics, and
• Third law of thermodynamics.

The Zeroth Law deals with thermal equilibrium and provides a means for measuring temperatures.

The First Law deals with the conservation of energy and introduces the concept of internal energy.

The Second Law of thermodynamics provides with the guidelines on the conversion of internal energy of matter into work. It also introduces the concept of entropy.

The Third Law of thermodynamics defines the absolute zero of entropy. The entropy of a pure crystalline substance at absolute zero temperature is zero.


¤ Different Approaches in the Study of Thermodynamics:

There are two ways through which the subject of thermodynamics can be studied

• Macroscopic Approach
• Microscopic Approach

¤ Macroscopic Approach:

Consider a certain amount of gas in a cylindrical container. The volume (V) can be measured by measuring the diameter and the height of the cylinder. The pressure (P) of the gas can be measured by a pressure gauge. The temperature (T) of the gas can be measured using a thermometer. The state of the gas can be specified by the measured P, V and T . The values of these variables are space averaged characteristics of the properties of the gas under consideration. In classical thermodynamics, we often use this macroscopic approach. The macroscopic approach has the following features.

• The structure of the matter is not considered.
• A few variables are used to describe the state of the matter under consideration. The values of these variables are measurable following the available techniques of experimental physics.

¤ Microscopic Approach:

On the other hand, the gas can be considered as assemblage of a large number of particles each of which moves randomly with independent velocity. The state of each particle can be specified in terms of position coordinates ( x_i , y_i , z_i ) and the momentum components ( p_xi , p_yi , p_zi ). If we consider a gas occupying a volume of 1 cm³ at ambient temperature and pressure, the number of particles present in it is of the order of 10²⁰. The same number of position coordinates and momentum components are needed to specify the state of the gas. The microscopic approach can be summarized as:

• A knowledge of the molecular structure of matter under consideration is essential.
• A large number of variables are needed for a complete specification of the state of the matter.

¤ Zeroth Law of Thermodynamics: 

This is one of the most fundamental laws of thermodynamics. It is the basis of temperature and heat transfer between two systems. Suppose we take three thermodynamic system named System A, System B and System C. Now let that system A is in thermal equilibrium with system B. By thermal equilibrium we mean that there is no heat transfer between system A and system B when they are brought in contact with each other. Now, suppose system A is in thermal equilibrium with system C too and there is no contact between system B and system C. It implies that although system B and C are isolated from each other, they will remain at thermal equilibrium to each other. It means that there will be no heat transfer between system B and C, when they are brought in contact with each other. This is called the Zeroth Law of thermodynamics.


¤ Basis of Temperature: 

When two bodies are kept at contact with each other and if there is no heat transfer between them we say that their body temperatures are same. It means that temperature is the property of a system which decides whether there will be any heat transfer between two different bodies. Heat transfer always occur from a higher temperature body to a lower temperature body. Further whenever there is any heat inflow to a body, it raises its temperature and conversely, if heat outflow occurs from a system it lowers its temperature.

Suppose we take two bodies one of which is at higher temperature than the other. Now when we bring the bodies at contact, heat will be transformed from a higher temperature body to that of lower temperature. Then what will be its effect, we may ask as a result of this heat transfer? Is this heat transfer a perpetual process? Our common life experiences tell us that it will not be the case. Although, at first heat transfer will take place, but its amount will be gradually decreased and after some time, a situation will come when there will be no heat transfer between the bodies or the bodies will come to a state of thermal equilibrium with each other. So, what is the reason for that? Can we justify the situation?

Yes, we can justify it as the hotter body releases heat to the colder body, the temperature of the hotter body decreases where as the temperature of the colder body increases and after sufficient time both the bodies will have equal temperature and a state of thermal equilibrium will be achieved.


¤ Temperature Measurement: 

We know the temperature of a body can be measured with a thermometer. How can we actually calculate the temperature of a body with the help of thermodynamics?


¤ Thermometer:

A thermometer is a temperature measuring instrument. It is made of a thin capillary glass tube, one end is closed and the other end is fitted with metallic bulb full of mercury. The mercury is in thermal equilibrium with the metallic bulb. Therefore, the temperature of the mercury is equal to the temperature of the metallic bulb. 
Mercury has a good coefficient of volume expansion and it means that as the temperature of the mercury increases, its volume increases too and as a result mercury column inside the capillary rises up. 

The capillary tube has been graduated with the help of calibrating with standard temperature sources. Therefore, the temperature of the mercury can be measured from the height of mercury column as the tube is finely graduated. 

Whenever we want to measure the temperature of a body, we kept the body in contact with the metallic bulb of the thermometer. When thermal equilibrium is established between the body and the metallic bulb of the thermometer, the temperature of both the body will be equal again the metallic bulb is in thermal equilibrium with mercury then the temperature of the mercury will be equal to the temperature of the metallic bulb and the temperature of the object.


As we can measure the temperature of the mercury from the column height, hence we can also determine the temperature of the object as they are equal to each other.

DISCUSSION:
Microscopic basis of temperature and pressure:
Here we shall try to discuss the basis of temperature and pressure only qualitatively, without any mathematical expression. 






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Thermodynamic Systems: 


If we want to analyze movement of energy over space, then we must define the space that would be used for the observation, we would call it as a System, separated from the adjoining space that is known as "Surroundings", by a boundary that may be real or may be virtual depending upon the nature of the observation. The boundary is called as System Boundary. So, we shall now define a system properly.


A thermodynamics system refers to a three dimensional space occupied by a certain amount of matter known as ''Working Substance'', and it is the space under consideration. It must be bounded by an arbitrary surface which may be real or imaginary, may be at rest or in motion as well as it may change its size and shape. All thermodynamic systems contain three basic elements:


• System boundary: The imaginary surface that bounds the system.
• System volume: The volume within the imaginary surface.
• The surroundings: The surroundings are everything external to the system.


So we get a space of certain volume where Energy Transfer (movement of energy) is going on, what may or may not be real, and distinct, it may be virtual (in case of flow system ), again if real boundary exists, then it may be fixed (rigid boundary like constant volume system) or may be flexible (like cylinder-piston assembly). For a certain experiment the system and surroundings together is called Universe.

The interface between the system and surroundings is called as "System boundary", which may be real and distinct in some cases where as some of them are virtual, but it may be real, solid and distinct. If the air in this room is the system, the floor, ceiling and walls constitutes real boundaries. The plane at the open doorway constitutes an imaginary boundary.



Classification of Thermodynamic Systems:

Systems can be classified as being (i) closed, (ii) open, or (iii) isolated.

(i) Closed System:

A thermodynamic system may exchange mass and energy with its surroundings. There are systems which allow only energy transfer with surroundings in the form of either heat transfer or work transfer or both heat and work transfer between a system and its surroundings. In these types of system, any sorts of mass transfer between the system and its surroundings are prohibited. These types of systems are classified as closed system. Examples of closed thermodynamic systems include a fluid being compressed by a piston inside a cylinder, a bomb calorimeter. In a closed system although energy content may vary over a period of time, but the system will always contain the same amount of matter.

(ii) Open System or Control Volume: 

An open system is a region in space defined by a boundary across which matter may flow in addition to work and heat exchange between the system and the surroundings. So, in an open system, the boundaries must have one or more opening through which mass transfer may take place in addition to work and heat transfer. Most of the engineering devices are examples of open system. Some examples are (a) a gas expanding from a container through a nozzle, (b) steam flowing through a turbine, and (c) water entering a boiler and leaving as steam. The boundary of an open system may be real or imaginary and it is called as control surface. The space inside an open system is called as control volume.

(iii) Isolated System:  

In an isolated system, there is no interaction between a system and its surroundings. Hence, the quantities of mass and energy in these types of system doesn’t change with time or we can say mass and energy remain constant in an isolated system. If there is no change in energy of a system, it indicates that there is neither any kind of heat transfer nor any kind of work transfer.  Our universe as a whole can be regarded as an isolated system.

Property, Equilibrium and State: 

A property is any measurable characteristic of a system. The common properties include: 

• pressure (P)

• temperature (T)

• volume (V)

• velocity (v)

• mass (m)

• enthalpy (H)

• entropy (S)

Properties can be intensive or extensive. Intensive properties are those whose values are independent of the mass possessed by the system, such as pressure, temperature, and velocity. Extensive properties are those whose values are dependent of the mass possessed by the system, such as volume, enthalpy, and entropy. 

Extensive properties are denoted by uppercase letters, such as volume (V), enthalpy (H) and entropy (S). Per unit mass of extensive properties are called specific properties and denoted by lowercase letters. For example, specific volume v = V/m, specific enthalpy h = H/m and specific entropy s = S/m 

*Note that work and heat are not properties. They are dependent of the process from one state to another state.

When the properties of a system are assumed constant from point to point and there is no change over time, the system is in a thermodynamic equilibrium.

The state of a system is its condition as described by giving values to its properties at a particular instant. For example, gas is in a tank. At state 1, its mass is 2 kg, temperature is 160°C, and volume is 0.1 m3. At state 2, its mass is 1 kg, temperature is 80°C, and volume is 0.2  m³..

A system is said to be at steady state if none of its properties changes with time.

State:

It is the condition of a system as defined by the values of all its properties. It gives a complete description of the system. Any operation in which one or more properties of a system change is called a change of state.

Phase:

It is a quantity of mass that is homogeneous throughout in chemical composition and physical structure. Examples of phase are solid, liquid, vapour, gas. Phase consisting of more than one phase is known as heterogenous system, where as if it consists of only one phase, it is called as homogenous system.

Process, Path and Cycle: 

The changes that a system undergoes from one equilibrium state to another are called a process. The series of states through which a system passes during a process is called path.

In thermodynamics the concept of quasi-equilibrium processes is used. It is a sufficiently slow process that allows the system to adjust itself internally so that its properties in one part of the system do not change any faster than those at other parts.

When a system in a given initial state experiences a series of quasi-equilibrium processes and returns to the initial state, the system undergoes a cycle. For example, the piston of car engine undergoes Intake stroke, Compression stroke, Combustion stroke, Exhaust stroke and goes back to Intake again. It is a cycle.

Quasi-static Processes:

Although the processes can be restrained or unrestrained, in practical purpose we need restrained processes.

A quasi-static process is one in which,

• The deviation from thermodynamic equilibrium is infinitesimal.

• All states of the system passes through are equilibrium states.

In a cylinder-piston assembly, several small weights are placed on the piston as shown in the figure. If we remove a weight, the pressure on the enclosed gas will be reduced by an infinitesimal amount. If we remove these weights one by one very slowly, then the pressure on the gas will be reduced by very small amount very slowly. Every time we remove a weight, the equilibrium state will be changed to a new equilibrium state at a very slow rate, such that the system will be appeared at a static condition as the change is infinitesimally small and the rate of change is also very small. The path of the change will be a series of quasi-equilibrium states. These types of processes are known as quasi-static processes.  

Equilibrium States:

A system is said to be in an equilibrium state if its properties will not be changed without some perceivable effect in the surroundings.

• Equilibrium generally requires all properties to be uniform throughout the system.

• There are mechanical, thermal, phase, and chemical equilibrium.

Nature has a preferred way of directing changes. As examples, we can say,

• Water flows from a higher to a lower level

• Electricity flows from a higher potential to a lower one

• Heat flows from a body at higher temperature to the one at a lower temperature

• Momentum transfer occurs from a point of higher pressure to a lower one.

• Mass transfer occurs from higher concentration to a lower one


Equilibrium state will be achieved when there will not be any change of the values of the properties of a system. Neither the system will exchange 
Heat Energy nor any Work exchange nor any kind of mass exchange with its surroundings. There are mainly three kind of Equilibrium and they are as follows.

* Thermal Equilibrium
* Mechanical Equilibrium
* Chemical Equilibrium


Thermal Equilibrium: 

When two bodies are in contact, there will be heat exchange between the bodies if and only there exists a temperature difference (ΔT) between the bodies.

Due to the temperature difference between the bodies, heat will flow from the high temperature body to the low temperature body. 

As a result of this heat transfer, the temperature of the hot body will be decreased and the temperature of the cold body will be increased.

When the temperature of both the bodies becomes equal to each others, the flow of heat stops. This equilibrium condition is known as the Thermal Equilibrium. 


Mechanical Eqiilibrium : 

If there exists a pressure gradient (ΔP) inside a system, between two systems or between a system and its surroundings, then the interface surface will experience a net force not equal to zero and due to which work transfer will happen where the system having higher pressure will do work against the lower pressure system. 

Due to this work transfer, pressure of the high pressure system will be decreased as energy has flown out of the system. On the other hand, the pressure in the low pressure system will be increased. When the pressure becomes equal in both sides, the work energy flow will be stopped and this state is known as the state of Mechanical Equilibrium.;

Chemical Equilibrium:

If there exists a chemical potential (Δμ) within the components of the system or between the system and surroundings, then there will be a spontaneous chemical reaction which will try to neutralize the chemical potential, after sometimes when the chemical potential becomes zero, the reaction stops and then there will not be any more changes in chemical properties of the system. This condition is called Chemical Equilibrium.

When a system attains thermal, mechanical and chemical equilibrium simultaneously, the state of the system is called in a "THERMODYNAMIC EQUILIBRIUM".

IC ENGINES: A CONCEPTUAL ANALYSIS

• INTRODUCTION: 

The idea of engines come from heat engines. Expanding steam was the working substance of the primitive kind of Steam Engines. But, locomotion was tough using steam engines as it needed continuous supply of water and coal as fuel. People started to think about a compact engines, light and portable and combustion will be the basis of heat generation. If heat generation could be taken place inside the cylinder, then it will be easier to design a compact engine which could be used to run a locomotive vehicle.

This semester, I am teaching IC Engines and Compressors. The text book is selected as IC Engines by Sharma and Mathur published by Dhanpat Rai Publications. The course is designed by MTU (Mahamaya Technical University, Noida and Gautam Budh Technical University) and it is taught in 5th semester. Although it is a 50 marks paper, still it is a subject which every Mechanical Engineering students must know. It is completely based on the principles of thermodynamics.

The course starts with defining IC Engines, introducing the components used in IC engines, different terms and processes related with IC engines, general working procedures of an IC engine and at last describing the classification of IC engines. Then the thermodynamic analysis of the engine operations along with Air-standard thermodynamic cycles are studied. If any one wants to know the subject deeply, then he should know very basic concepts of thermodynamics. 

• PRE-REQUISITE KNOWLEDGE:

As air-standard cycles are one of the basic models based on which engines are practically run and is a highly simplified or even oversimplified version of the original engine operation and due to this, the experimental values of the engine efficiencies are much below the value predicted by the air standard cycles. The large amount of deviations of actual cycles from the theoretical air standard cycles are due to assumptions taken during air standard cycle analysis.

• DESCRIPTION OF THE IC ENGINE:

While describing IC engines, one should start with the engine cylinder which acts as the combustion chamber which has a variable volume due to a piston which can slide inside the cylinder. 

One end of the cylinder is sealed off by cylinder head which provides the space for clearance volume and it also housed the inlet and exhaust valves. 

The other end of the cylinder is covered by the piston which can slide along the principal axis of the cylinder. 

Inside the cylinder air-fuel mixture is sucked into and then compressed it in case of SI engines, where as in CI engine only air is sucked into the cylinder. 

The piston is connected to a link known as Connecting rod by a pin named Gudgeon or Piston or Wrist pin. 

This connecting rod has unequal ends. The smaller end is connected to piston by gudgeon pin and the bigger end is connected to the eccentric on the Crank. 

It is joined to the eccentric by a pin named Crank pin. Piston, Connecting Rod and Crank constitute a "Slider-Crank Mechanism" which translates a linear "to and fro motion" of the piston into "rotational motion" of the crank. 

Here, connecting rod is the element that bears the whole load, hence it fails quite frequently. 

Crank is mounted on a crank shaft and crank shaft operates two valve mechanism through poppet valve, rocket arm and cams. 

These valve mechanisms are responsible for the opening and closing of inlet as well as exhaust valves. 

This valves are regulated by cams. Cams are mounted on a cam shaft which is geared with crankshaft by a step down gear mechanism so that for every two revolutions of crankshaft rotation the camshaft makes one rotation. So, the complete thermodynamic cycle of two crankshaft rotation crankshaft makes only one cycle. The idea behind this step down mechanism, is valves are needed to open and close once in a complete thermodynamic cycle and a cam profile can be designed easily. 

A flywheel is mounted on the crankshaft, so that it can absorb and store energy during power stroke or expansion stroke and releases energy to power suction, compression and exhaust stroke.

In SI engine, after the end of compression stroke, the pressure and temperature of the air-fuel mixture becomes sufficiently high to sustain the ignition process after ignition takes place. After the compression pressure becomes 10 to 12 bar and temperature becomes 300^o C to 500^o C. It is still below the temperature at which spontaneous auto-ignition generally starts. If the temperature after compression is above the temperature at which auto ignition starts, then auto ignition will start during the last phases of compression stroke and it will create an explosion known as knocking and detonation.

Then theoretical basis of an IC engines are discussed. While analyzing any phenomena, the best way is to make an idealized modelling of the phenomena by considering certain assumptions which would reduce the complexity of the phenomena and make a oversimplified model and then add the complexity one by one. 

Similarly, here we oversimplified the model of IC engine operation by considering the working substance an ideal gas like air and study some reversible thermodynamic cycles those resemble with the processes those occurs inside an IC engine. 

As those cycles are considered having air as working substance and hence, they are called Air-Standard cycles. But, as Air-Standard Cycle are the idealized version of the real life working principle of an IC engines, its analysis can not be used to gauge the performances of the engine with closest accuracy.

 
Thermodynamic Air-standard cycles like Otto, Diesel, Dual, Stirling and Ericsson cycles are discussed. 

Derivation of total work done, Efficiency, Mean Effective Pressure and graphs in p-v and T-s diagrams are studied.

 
In the air standard cycles, working substance is assumed to be perfect gas like pure air, but in actual cycles the working substance is different and it is the mixture of air and fuels. In air standard cycle it is assumed that specific heats are constant where as in reality, specific heats are functions of temperature and it increases with the increase of temperature. 

Moreover, in air standard cycle, it is assumed that working substance is chemically non-reactive and there is no chemical changes inside the engine cylinder, but in reality, inside the cylinder combustion process takes place and the chemical composition of the working substance rapidly changes during the combustion process which alters the composition as well as number of moles of the working substances also got changed.

The combined effect of both the phenomena is to reduce the temperature and pressure after the end of compression stroke as well as it reduces the maximum cycle temperature and pressure after the end of combustion. 

While expanding adiabatically during the power stroke, the temperature and pressure after expansion is higher than the predicted value according to air standard cycle and as a result it increases the value of rejected heat into the thermal sink. 

Therefore, the actual cycle efficiency is much lower than the air standard cycle efficiency. Moreover, there are several other losses during the actual cycle due to various other design limitations. The major losses are 

• (i) burning time losses, 
• (ii) losses due to incomplete combustion, 
• (iii) Direct heat losses due to colder cylinder and heat carried away by coolants, 
• (iv) pumping losses, 
• (v) friction losses due to rubbing of parts, 
• (vi) blow down losses during exhaust.

So, we have first idealized the engine operations and oversimplified it to have an idealized version, but its prediction will not be accurate, but we shall get an upper limit of the efficiencies of IC engines. Now, to get more accurate analysis, we shall modified the simplistic assumptions we have considered during the air standard cycles analysis.

The most important assumption of the air standard cycle is the choosing pure air as our working substance, which is in reality a mixture of air with fuel, which has been mixed homogeneously in the carburettor and then supplied into the engine cylinder which acts as combustion chamber. Therefore, we first substitute air with the air fuel mixture in the air standard cycles and it is hence called "Fuel Air Cycles".

Due to the replacement of working substance by air fuel mixture in stead of pure air, our two key assumptions have been changed too. First of all, fuel-air mixture doesn't show a constant specific heats in stead specific heats are functions of temperature, linearly at low temperatures, non linearly at high temperatures.

C_p = aT² + bT + k

C_v = cT² + dT + k'

ASSUMPTIONS CONSIDERED IN ANALYZING AIR STANDARD CYCLE:

AIR STANDARD CYCLE:

• In true sense, internal combustion engines in which combustion of fuels occurs inside the engine cylinder can not be defined as cyclic heat engines. The temperature generated during combustion is very high so that engines must be water cooled to prevent the damage of the engine due to thermal shock. The working fluid here is a mixture of air and fuel that undergoes permanent chemical changes due to combustion and the products of combustions must be exhausted and driven out of the cylinder so that fresh charges can be admitted. Therefore, it does not complete a full thermodynamic cycle.
• The engine cycle analysis is an important tool in the design and study of
• Internal Combustion Engines. 
•  A thermodynamic cycle is defined as a series of processes through which the working fluid progresses and ultimately return to the original state. 
•  Although the thermodynamic cycles are closed cycles and actual engine 
• A real thermodynamic analysis of such an engine quite complex. Hence, we simplified the operation of an I.C. Engine by introducing somewhat idealized version of a real thermodynamic processes occur inside an IC Engine, and this idealized thermodynamic cycles are called "Air standard cycle." In an air standard cycle, a certain mass of a perfect gas like air operates in a complete thermodynamic cycle, where heat is added and rejected reversibly with external heat reservoirs, and all the processes in the cycle are reversible. Air is assumed to behave like a perfect gas, and like a perfect gas, its specific heats are assumed to be constant (although they are certain functions of temperature). These air standard cycles are conceived in such a manner that they may correspond to the operations of internal combustion engines.
•  Although, there are numerous such air standard cycles, the important of them are

a) Otto Cycle (used for petrol engine)

b) Diesel Cycle (used for diesel engine)

c) Mixed, limited pressure or Dual Cycle (used for hot spot engine)

d) Stirling Cycle

e) Ericsson Cycle

To make the analysis simpler, certain assumptions are made during the analysis of air standard cycle. They are as following,

• i) The working substance is a perfect gas obeying the gas equation pV = mRT.
• ii) The working fluid is a fixed mass of air either contained in a closed system or flowing at a constant rate round a closed cycle.
• iii) The physical constants of the working fluid will be those of air.
• iv) The working medium has constant specific heats.
• v) The working media doesn't undergo any chemical change throughout the cycle.

OTTO CYCLE:

The Otto cycle is a thermodynamic cycle used in gasoline (petrol) engines to convert the chemical energy stored in fuel into useful work. It is a four-stroke cycle, consisting of four processes: intake, compression, combustion, and exhaust.

During the intake stroke, the fuel-air mixture is drawn into the engine cylinder as the piston moves downward. During the compression stroke, the mixture is compressed by the upward motion of the piston, which raises the temperature and pressure of the mixture. Near the end of the compression stroke, the spark plug ignites the mixture, causing a rapid combustion that generates a high-pressure wave that drives the piston downward, producing power. This is the power stroke. Finally, during the exhaust stroke, the spent gases are expelled from the cylinder as the piston moves upward.

The Otto cycle is an idealized model of the engine, assuming that the combustion occurs instantaneously and that there are no losses due to friction, heat transfer, or other factors. In practice, real engines operate less efficiently than the idealized model, due to these losses.

The Otto cycle is named after its inventor, Nikolaus Otto, a German engineer who patented the four-stroke engine in 1876. The cycle is widely used in modern gasoline engines, which have been refined and optimized over more than a century of development to achieve high levels of performance, efficiency, and reliability.

DIESEL CYCLE:

The Diesel cycle is a thermodynamic cycle used in diesel engines to convert the chemical energy stored in fuel into useful work. It is a four-stroke cycle, consisting of four processes: intake, compression, combustion, and exhaust.

During the intake stroke, air is drawn into the engine cylinder as the piston moves downward. During the compression stroke, the air is compressed by the upward motion of the piston, which raises the temperature and pressure of the air. Near the end of the compression stroke, fuel is injected into the cylinder, which ignites due to the high temperature and pressure of the air. The fuel-air mixture combusts, generating a high-pressure wave that drives the piston downward, producing power. This is the power stroke. Finally, during the exhaust stroke, the spent gases are expelled from the cylinder as the piston moves upward.

The Diesel cycle is similar to the Otto cycle but differs in that it does not rely on a spark plug to ignite the fuel. Instead, the fuel is injected directly into the cylinder and ignites due to the heat of the compressed air. This allows diesel engines to operate at a higher compression ratio than gasoline engines, which leads to higher efficiency and better fuel economy.

The Diesel cycle is named after Rudolf Diesel, a German inventor who patented the diesel engine in 1892. Diesel engines are widely used in a variety of applications, including cars, trucks, buses, ships, and generators. They are known for their efficiency, durability, and reliability.

Mixed, limited pressure or Dual Cycle (used for hot spot engine):

The Mixed or Dual Cycle is a thermodynamic cycle used in hot-spot engines, which are a type of internal combustion engine that combines elements of diesel and gasoline engines. The cycle is also sometimes referred to as the Limited Pressure cycle.

The Dual Cycle is a combination of the Otto and Diesel cycles. It uses the diesel combustion process, where fuel is injected directly into the cylinder and ignited by the heat of compressed air, but also includes a spark plug like in the Otto cycle. During the intake stroke, air is drawn into the cylinder, and during the compression stroke, the air is compressed to a higher pressure and temperature than in the Otto cycle. Fuel is injected into the cylinder, and the spark plug ignites the fuel-air mixture, creating a flame that spreads through the cylinder. The combustion of the fuel-air mixture produces high pressure and temperature, which drives the piston downward, producing power. Finally, during the exhaust stroke, the spent gases are expelled from the cylinder as the piston moves upward.

The Dual Cycle is designed to provide the advantages of both the diesel and gasoline engines, namely high efficiency and low emissions. It allows for a higher compression ratio than the Otto cycle, which leads to better fuel economy, while also reducing the emission of pollutants like nitrogen oxides (NOx) and particulate matter. The Dual Cycle is used in some specialized applications, such as large marine engines and certain military vehicles. However, it is not as widely used as the Otto and Diesel cycles in most everyday applications.

STERLING CYCLE:

The Stirling cycle is a thermodynamic cycle used in Stirling engines, which are a type of heat engine that converts heat energy into mechanical work. Unlike traditional internal combustion engines, Stirling engines operate on an external heat source, which can be supplied by any fuel source that can produce heat, such as wood, coal, or natural gas.

The Stirling cycle consists of four processes: heating, expansion, cooling, and compression. During the heating process, the working fluid (typically a gas such as helium or hydrogen) is heated by an external heat source, causing it to expand and drive a piston outward. During the expansion process, the expanding gas continues to drive the piston outward, producing mechanical work. During the cooling process, the working fluid is cooled by a heat sink (usually air or water), causing it to contract and pull the piston inward. Finally, during the compression process, the compressed gas is pushed back to the starting point, ready to begin the cycle again.

The Stirling cycle is designed to maximize efficiency by minimizing the losses associated with traditional internal combustion engines, such as friction and heat transfer. However, Stirling engines have a relatively low power-to-weight ratio and are less suitable for high-speed applications. They are typically used in specialized applications, such as in submarines, where quiet operation and long running times are important.

The Stirling engine was invented in the early 19th century by Robert Stirling, a Scottish clergyman, and engineer. Despite its potential benefits, the Stirling engine has not been widely adopted in mainstream applications due to its complexity and high cost compared to other types of engines. However, research and development continue to explore ways to improve the efficiency and practicality of Stirling engines.

CONCEPTS OF BASIC THERMODYNAMICS

¤ Introduction:

The most of general sense of thermodynamics is the study of energy and its relationship to the properties of matter. All activities in nature involve some interaction between energy and matter. Thermodynamics is a science that governs the following:

• (i) Energy and its transformation
• (ii) Feasibility of a process involving transformation of energy
• (iii) Feasibility of a process involving transfer of energy
• (iv) Equilibrium processes

More specifically, thermodynamics deals with energy conversion, energy exchange and the direction of exchange.

¤ Areas of Application of Thermodynamics:

All natural processes are governed by the principles of thermodynamics. However, the following engineering devices are typically designed based on the principles of thermodynamics.

Automotive engines, Turbines, Compressors, Pumps, Fossil and Nuclear Power Plants, Propulsion systems for the Aircrafts, Separation and Liquefaction Plant, Refrigeration, Air-conditioning and Heating Devices.

The principles of thermodynamics are summarized in the form of a set of axioms. These axioms are known as four thermodynamic laws:

• Zeroth law of thermodynamics,
• First law of thermodynamics,
• Second law of thermodynamics, and
• Third law of thermodynamics.

The Zeroth Law deals with thermal equilibrium and provides a means for measuring temperatures.

The First Law deals with the conservation of energy and introduces the concept of internal energy.

The Second Law of thermodynamics provides with the guidelines on the conversion of internal energy of matter into work. It also introduces the concept of entropy.

The Third Law of thermodynamics defines the absolute zero of entropy. The entropy of a pure crystalline substance at absolute zero temperature is zero.


¤ Different Approaches in the Study of Thermodynamics:

There are two ways through which the subject of thermodynamics can be studied

• Macroscopic Approach
• Microscopic Approach

¤ Macroscopic Approach:

Consider a certain amount of gas in a cylindrical container. The volume (V) can be measured by measuring the diameter and the height of the cylinder. The pressure (P) of the gas can be measured by a pressure gauge. The temperature (T) of the gas can be measured using a thermometer. The state of the gas can be specified by the measured P, V and T . The values of these variables are space averaged characteristics of the properties of the gas under consideration. In classical thermodynamics, we often use this macroscopic approach. The macroscopic approach has the following features.

• The structure of the matter is not considered.
• A few variables are used to describe the state of the matter under consideration. The values of these variables are measurable following the available techniques of experimental physics.

¤ Microscopic Approach:

On the other hand, the gas can be considered as assemblage of a large number of particles each of which moves randomly with independent velocity. The state of each particle can be specified in terms of position coordinates ( x_i , y_i , z_i ) and the momentum components ( p_xi , p_yi , p_zi ). If we consider a gas occupying a volume of 1 cm³ at ambient temperature and pressure, the number of particles present in it is of the order of 10²⁰. The same number of position coordinates and momentum components are needed to specify the state of the gas. The microscopic approach can be summarized as:

• A knowledge of the molecular structure of matter under consideration is essential.
• A large number of variables are needed for a complete specification of the state of the matter.

¤ Zeroth Law of Thermodynamics: 

This is one of the most fundamental laws of thermodynamics. It is the basis of temperature and heat transfer between two systems. Suppose we take three thermodynamic system named System A, System B and System C. Now let that system A is in thermal equilibrium with system B. By thermal equilibrium we mean that there is no heat transfer between system A and system B when they are brought in contact with each other. Now, suppose system A is in thermal equilibrium with system C too and there is no contact between system B and system C. It implies that although system B and C are isolated from each other, they will remain at thermal equilibrium to each other. It means that there will be no heat transfer between system B and C, when they are brought in contact with each other. This is called the Zeroth Law of thermodynamics.


¤ Basis of Temperature: 

When two bodies are kept at contact with each other and if there is no heat transfer between them we say that their body temperatures are same. It means that temperature is the property of a system which decides whether there will be any heat transfer between two different bodies. Heat transfer always occur from a higher temperature body to a lower temperature body. Further whenever there is any heat inflow to a body, it raises its temperature and conversely, if heat outflow occurs from a system it lowers its temperature.

Suppose we take two bodies one of which is at higher temperature than the other. Now when we bring the bodies at contact, heat will be transformed from a higher temperature body to that of lower temperature. Then what will be its effect, we may ask as a result of this heat transfer? Is this heat transfer a perpetual process? Our common life experiences tell us that it will not be the case. Although, at first heat transfer will take place, but its amount will be gradually decreased and after some time, a situation will come when there will be no heat transfer between the bodies or the bodies will come to a state of thermal equilibrium with each other. So, what is the reason for that? Can we justify the situation?

Yes, we can justify it as the hotter body releases heat to the colder body, the temperature of the hotter body decreases where as the temperature of the colder body increases and after sufficient time both the bodies will have equal temperature and a state of thermal equilibrium will be achieved.


¤ Temperature Measurement: 

We know the temperature of a body can be measured with a thermometer. How can we actually calculate the temperature of a body with the help of thermodynamics?


¤ Thermometer:

A thermometer is a temperature measuring instrument. It is made of a thin capillary glass tube, one end is closed and the other end is fitted with metallic bulb full of mercury. The mercury is in thermal equilibrium with the metallic bulb. Therefore, the temperature of the mercury is equal to the temperature of the metallic bulb. 
Mercury has a good coefficient of volume expansion and it means that as the temperature of the mercury increases, its volume increases too and as a result mercury column inside the capillary rises up. 

The capillary tube has been graduated with the help of calibrating with standard temperature sources. Therefore, the temperature of the mercury can be measured from the height of mercury column as the tube is finely graduated. 

Whenever we want to measure the temperature of a body, we kept the body in contact with the metallic bulb of the thermometer. When thermal equilibrium is established between the body and the metallic bulb of the thermoneter, the temperature of both the body will be equal again the metallic bulb is in thermal equilibrium with mercury then the temperature of the mercury will be equal to the temperature of the metallic bulb and the temperature of the object.


As we can measure the temperature of the mercury from the column height, hence we can also determine the temperature of the object as they are equal to each other.

DISCUSSION:
Microscopic basis of temperature and pressure:
Here we shall try to discuss the basis of temperature and pressure only qualitatively, without any mathematical expression. 






.....................contact me at email: subhankarkarma@gmail.com for more notes

BASICS OF THERMODYNAMICS

Thermodynamic Systems: 


If we want to analyze movement of energy over space, then we must define the space that would be used for the observation, we would call it as a System, separated from the adjoining space that is known as "Surroundings", by a boundary that may be real or may be virtual depending upon the nature of the observation. The boundary is called as System Boundary. So, we shall now define a system properly.


A thermodynamics system refers to a three dimensional space occupied by a certain amount of matter known as ''Working Substance'', and it is the space under consideration. It must be bounded by an arbitrary surface which may be real or imaginary, may be at rest or in motion as well as it may change its size and shape. All thermodynamic systems contain three basic elements:


• System boundary: The imaginary surface that bounds the system.
• System volume: The volume within the imaginary surface.
• The surroundings: The surroundings are everything external to the system.


So we get a space of certain volume where Energy Transfer (movement of energy) is going on, what may or may not be real, and distinct, it may be virtual (in case of flow system ), again if real boundary exists, then it may be fixed (rigid boundary like constant volume system) or may be flexible (like cylinder-piston assembly). For a certain experiment the system and surroundings together is called Universe.

The interface between the system and surroundings is called as "System boundary", which may be real and distinct in some cases where as some of them are virtual, but it may be real, solid and distinct. If the air in this room is the system, the floor, ceiling and walls constitutes real boundaries. The plane at the open doorway constitutes an imaginary boundary.



Classification of Thermodynamic Systems:

Systems can be classified as being (i) closed, (ii) open, or (iii) isolated.

(i) Closed System:

A thermodynamic system may exchange mass and energy with its surroundings. There are systems which allow only energy transfer with surroundings in the form of either heat transfer or work transfer or both heat and work transfer between a system and its surroundings. In these types of system, any sorts of mass transfer between the system and its surroundings are prohibited. These types of systems are classified as closed system. Examples of closed thermodynamic systems include a fluid being compressed by a piston inside a cylinder, a bomb calorimeter. In a closed system although energy content may vary over a period of time, but the system will always contain the same amount of matter.

(ii) Open System or Control Volume: 

An open system is a region in space defined by a boundary across which matter may flow in addition to work and heat exchange between the system and the surroundings. So, in an open system, the boundaries must have one or more opening through which mass transfer may take place in addition to work and heat transfer. Most of the engineering devices are examples of open system. Some examples are (a) a gas expanding from a container through a nozzle, (b) steam flowing through a turbine, and (c) water entering a boiler and leaving as steam. The boundary of an open system may be real or imaginary and it is called as control surface. The space inside an open system is called as control volume.

(iii) Isolated System:  

In an isolated system, there is no interaction between a system and its surroundings. Hence, the quantities of mass and energy in these types of system doesn’t change with time or we can say mass and energy remain constant in an isolated system. If there is no change in energy of a system, it indicates that there is neither any kind of heat transfer nor any kind of work transfer.  Our universe as a whole can be regarded as an isolated system.

Property, Equilibrium and State: 

A property is any measurable characteristic of a system. The common properties include: 

• pressure (P)

• temperature (T)

• volume (V)

• velocity (v)

• mass (m)

• enthalpy (H)

• entropy (S)

Properties can be intensive or extensive. Intensive properties are those whose values are independent of the mass possessed by the system, such as pressure, temperature, and velocity. Extensive properties are those whose values are dependent of the mass possessed by the system, such as volume, enthalpy, and entropy. 

Extensive properties are denoted by uppercase letters, such as volume (V), enthalpy (H) and entropy (S). Per unit mass of extensive properties are called specific properties and denoted by lowercase letters. For example, specific volume v = V/m, specific enthalpy h = H/m and specific entropy s = S/m 

*Note that work and heat are not properties. They are dependent of the process from one state to another state.

When the properties of a system are assumed constant from point to point and there is no change over time, the system is in a thermodynamic equilibrium.

The state of a system is its condition as described by giving values to its properties at a particular instant. For example, gas is in a tank. At state 1, its mass is 2 kg, temperature is 160°C, and volume is 0.1 m3. At state 2, its mass is 1 kg, temperature is 80°C, and volume is 0.2  m³..

A system is said to be at steady state if none of its properties changes with time.

State:

It is the condition of a system as defined by the values of all its properties. It gives a complete description of the system. Any operation in which one or more properties of a system change is called a change of state.

Phase:

It is a quantity of mass that is homogeneous throughout in chemical composition and physical structure. Examples of phase are solid, liquid, vapour, gas. Phase consisting of more than one phase is known as heterogenous system, where as if it consists of only one phase, it is called as homogenous system.

Process, Path and Cycle: 

The changes that a system undergoes from one equilibrium state to another are called a process. The series of states through which a system passes during a process is called path.

In thermodynamics the concept of quasi-equilibrium processes is used. It is a sufficiently slow process that allows the system to adjust itself internally so that its properties in one part of the system do not change any faster than those at other parts.

When a system in a given initial state experiences a series of quasi-equilibrium processes and returns to the initial state, the system undergoes a cycle. For example, the piston of car engine undergoes Intake stroke, Compression stroke, Combustion stroke, Exhaust stroke and goes back to Intake again. It is a cycle.

Quasi-static Processes:

Although the processes can be restrained or unrestrained, in practical purpose we need restrained processes.

A quasi-static process is one in which,

• The deviation from thermodynamic equilibrium is infinitesimal.

• All states of the system passes through are equilibrium states.

In a cylinder-piston assembly, several small weights are placed on the piston as shown in the figure. If we remove a weight, the pressure on the enclosed gas will be reduced by an infinitesimal amount. If we remove these weights one by one very slowly, then the pressure on the gas will be reduced by very small amount very slowly. Every time we remove a weight, the equilibrium state will be changed to a new equilibrium state at a very slow rate, such that the system will be appeared at a static condition as the change is infinitesimally small and the rate of change is also very small. The path of the change will be a series of quasi-equilibrium states. These types of processes are known as quasi-static processes.  

Equilibrium States:

A system is said to be in an equilibrium state if its properties will not be changed without some perceivable effect in the surroundings.

• Equilibrium generally requires all properties to be uniform throughout the system.

• There are mechanical, thermal, phase, and chemical equilibrium.

Nature has a preferred way of directing changes. As examples, we can say,

• Water flows from a higher to a lower level

• Electricity flows from a higher potential to a lower one

• Heat flows from a body at higher temperature to the one at a lower temperature

• Momentum transfer occurs from a point of higher pressure to a lower one.

• Mass transfer occurs from higher concentration to a lower one


Equilibrium state will be achieved when there will not be any change of the values of the properties of a system. Neither the system will exchange 
Heat Energy nor any Work exchange nor any kind of mass exchange with its surroundings. There are mainly three kind of Equilibrium and they are as follows.

* Thermal Equilibrium
* Mechanical Equilibrium
* Chemical Equilibrium


Thermal Equilibrium: 

When two bodies are in contact, there will be heat exchange between the bodies if and only there exists a temperature difference (ΔT) between the bodies.

Due to the temperature difference between the bodies, heat will flow from the high temperature body to the low temperature body. 

As a result of this heat transfer, the temperature of the hot body will be decreased and the temperature of the cold body will be increased.

When the temperature of both the bodies becomes equal to each others, the flow of heat stops. This equilibrium condition is known as the Thermal Equilibrium. 


Mechanical Eqiilibrium : 

If there exists a pressure gradient (ΔP) inside a system, between two systems or between a system and its surroundings, then the interface surface will experience a net force not equal to zero and due to which work transfer will happen where the system having higher pressure will do work against the lower pressure system. 

Due to this work transfer, pressure of the high pressure system will be decreased as energy has flown out of the system. On the other hand, the pressure in the low pressure system will be increased. When the pressure becomes equal in both sides, the work energy flow will be stopped and this state is known as the state of Mechanical Equilibrium.;

Chemical Equilibrium:

If there exists a chemical potential (Δμ) within the components of the system or between the system and surroundings, then there will be a spontaneous chemical reaction which will try to neutralize the chemical potential, after sometimes when the chemical potential becomes zero, the reaction stops and then there will not be any more changes in chemical properties of the system. This condition is called Chemical Equilibrium.

When a system attains thermal, mechanical and chemical equilibrium simultaneously, the state of the system is called in a "THERMODYNAMIC EQUILIBRIUM".