When I joined IEC College of Engg & Technology in 1999, for the first time I heard of Richard Feynman & his style of writings. His three volume Lectures on Physics changed me permanently. The language was lucid and he told about the facts of Physics just like a thriller novel. I became a diehard fan of Physics and Feynman.
These piece of article on thermodynamic concept is an earnest try to tell about energy mechanics as a story.
CONCEPTUAL IDEAS :
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 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 & surroundings is called as "SYSTEM BOUNDARIES", which may be real & distinct in some cases where as some of them are virtual, but it may be real, solid and distinct.
ENERGY:
Although we can't exactly define what is Energy, yet we can say how does Energy behave, even we can measure the change in energy of the system, we may say that Energy always posses the capability to do certain amount of work depending upon the form of Energy. We can also describe the different forms of Energy those can exist like potential energy, kinetic energy, chemical energy, binding energy, nuclear energy etc.
Depending upon the capacity to do work, energy can be classified into different forms. If the energy is highly ordered then it is HIGH GRADE ENERGY, like Kinetic Energy, where as when Energy exists in a chaotic form we call it LOW GRADE ENERGY. Heat energy of a body arises due to random motions of the individual molecules. Hence we can say that HEAT ENERGY is related with the chaosness of the molecules, therefore, it is the most low grade energy.
HEAT TRANSFER :
Through the boundary, a system and its surroundings can exchange energy between them, if allowed by the boundary properties. There are three modes of energy interaction a system and surroundings. If the boundaries are permeable to allow heat flow across it, then the energy transfer mode is called HEAT TRANSFER.
When a system absorbs heat energy from the surroundings due to the temperature difference between system and surroundings the transfer of energy is named as HEAT TRANSFER.
WORK TRANSFER :
When a system has a flexible or movable boundary then energy can be transfer by virtue of workdone. If there exists a pressure gradient between a system and its surroundings then work exchange takes place between the system and the surroundings as the flexible boundary moves to destroy the pressure gradient that exists between the system and the surroundings. So we would say the Energy Transfer due to pressure gradient is named as WORK TRANSFER.
MASS TRANSFER :
For flow process in a open system, mass transfer takes place between system & surroundings which is the third type of Energy Transfer and named as Mass Transfer. Any open system has two passages for fluid flow. Through one passage, the mass of the working substance enters into the system and aptly named as INLET, while the second passage is used by the working fluid to flow out of the system and it is named as OUTLET. So, in open system mass flow occurs across the system and this phenomenon of mass inflow and outflow from the system is named as MASS TRANSFER between a system and it's boundaries.
CONCEPTS OF MASS :
What is mass? Or we can say what is it to be a substance? Here, again we face the fundamental difficulty to define Mass accurately, although we know how it does behave, we can measure its value even, but it is really not clear what is mass made of. When Einstein equates mass in terms of energy, it defines mass as a form of energy but they are bound within the mass which again consists of elementary but composite particles named electron, proton & neutron. Proton, neutrons are made of QUARKS, which are the most fundamental particles of nature. Although Quarks are already well researched, and we know the most possible reason of the “confinement” phenomenon, still there exists a large number of physical phenomenon which can be explained using the “standard model of particle physics”.
PROPERTIES OF A SYSTEM :
A system is characterized by the values of its properties. So the most logical question that would arise here would be about properties of a system. So what is a property of a system? It has been seen that every object that exists in this Universe possesses some physical & chemical characteristics, like size, shape, mass, energy, chemical composition, colors etc. Among these various characteristics, those are related with energy directly or indirectly are called as "thermodynamic functions". There are mainly two types of thermodynamic functions, which can be better described in mathematical terms as they are physical quantity and hence are measurable. Here we shall take a little hiatus (break) to know some facts about physical quantity.
Physical characteristics are of two types. Any physical characteristics can be represented by the mathematical quantity and it is thus represented by mathematical functions. There may be two types of mathematical functions. When expressed in differential form, some of the functions become Exact differential and some of them produces In-exact differential form. The exact differential functions are called as thermodynamic properties. They are also known as “Point Functions”. Where as the in-exact differentials are called “Path Functions”
EQUILIBRIUM CONDITIONS :
Every thermodynamic function are directly or indirectly measurable and when there is no energy transfer between the system and surroundings, then the value of the functions assume a certain value by which we can specify the state or condition of a thermodynamic system. So, the values are only measurable when they are not changing over a period of time. What does it implicate that the values of the thermodynamic functions are not continuously changing. When the values are not changing it indicates a stability of the state of the system over a certain periods of time. This stability of a system implies an Equilibrium condition. Each and every equilibrium states are distinct and they are specified by the distinct value of the properties of the system at that equilibrium conditions.
CONCEPTS OF A THERMODYNAMIC PLANE :
A thermodynamics system is a bi-variate function. It means that to specify a thermodynamic system we need to specify the values of any two properties. One can also describe a thermodynamic system has two degrees of freedom. So, mathematically, we can say that any thermodynamic system at a certain equilibrium condition can be represented as a point on a two dimensional plane. The plane thus formed plotting thermodynamic properties along X and Y axes of a Cartesian Coordinate system is known as thermodynamic plane.
A point on this plane represents a system at a thermodynamic equilibrium condition, which can be defined as a state which is time invariant when it is isolated from the surroundings. So, at equilibrium condition the values of different thermodynamic properties remain constant over a considerable amount of time.
EXTERNAL DISTURBANCES AND CHANGE OF STATE OF A SYSTEM:
We have already know that when the values of different thermodynamic properties become stable we get an equilibrium state where no values of the properties can be changed without application of any external influences. But, what happens, when an external agency tries to change the values of the properties of the system. Here, what does it mean by "external influences"? What does it mean in real life? We know from our daily life experiences that any kind of external influences can be at last reduced to any kind of force only and the use of external influences always lead to an exchange of energy between the system and the surroundings. To explain the phenomena we shall take a system at equilibrium with its surroundings. Hence, the pressure P and temperature T of both the system as well as the surroundings too. Now, to disturb the equilibrium condition of the system we must change either the pressure or the temperature of the system. Suppose we take a cylinder-piston assembly, whose temperature is T and pressure is P. Now suppose, we inject a small amount of energy very slowly into the system, can you tell, what type of change we should expect in this case.
Suppose we change the pressure from (P) to (P + dP) where (dP) is the change of pressure of the system, where as the pressure of the surroundings remains at (P). Then there exists a pressure difference of the flexible wall that separates our system from its surroundings. As a result a force will act on the flexible wall of the system, and the wall will move along the net force on it. Therefore, an amount of work done will be there due to the displacement of the boundary wall. There may be two type of cases, when (dP) is positive, the system does work on the surrounding as the volume of the system increases. As the volume increases from V to (V + dV) the pressure would drop to (P) from (P + dP). Hence due to this energy transfer from the system to surrounding again Equilibrium will be achieved.
VARIABLES IN THERMODYNAMICS
STATE AND COMPOSITION OF MATTER :
From our common sense we can say that matters are composed of mass, a fundamental form of energy. From our early experimentation with mass and nature, we could conclude a concept of mass as a continuous physical quantity, it implies that we can divide any quantity of mass, whatever small it may be. This view is essentially evolved on the basis of our macro world perception.
But within few years rapid growth of modern science shows that our perception of a continuous character of mass is an incorrect idea. Hence particle character was bestowed on mass that tells us that masses are made of tiny particles, that can independently exist in a stable condition and nicely named as molecules which are different for different materials. But it is not the fundamental particles of mass. There are more to come!
So, a piece of matter is really made of very large numbers of stable molecules, which scientists conclude is made of atoms. Again atoms are composed of very tiny fundamental negatively charged particles named electrons, and the core of the atoms are called as nucleus is made of chargeless neutrons and positively charged protons.
So mass is a discontinuous physical quantity and microscopic by nature! But our common perception says that it is a continuum and hence macroscopic by nature. Accordingly, there are two ways to learn thermodynamics, one is macroscopic approach, also known as Classical
Thermodynamics. and the other was named as Statistical Thermodynamics. It is basically Energy Dynamics at microscopic level.
ENERGY
The focus of Thermodynamics: As the name suggests, is primarily on energy, more specifically heat energy and related variable.(Thermos means Heat energy and Temperature).
So, first thermodynamic property is Energy itself! We use the term so frequently that we never think about its proper definition and understanding. Let me ask you one thing when someone mentions that he or she is feeling more energetic, what does he actually want to mean? In simple terms we can specify Energy as "something" that has the capacity to do work. Therefore, we can say that Energy has the capacity to do work, whatever it may be the change of anything is some way or other is connected with the exchange of Energy between bodies.
STORED ENERGY AND ENERGY IN TRANSITION :
We have defined thermodynamics as the knowledge of Energy and its movement in the space, including the dynamics of the involved mechanisms and processes. So, our prime interest would be Energy here, hence Energy must be defined as a physical quantity (hence can be measured), which has the capacity to perform useful work against any resistance.
Here, the definition of work must be given, as thermodynamic work is different from mechanical work.
MECHANICAL WORK Vs. THERMODYNAMIC WORK:
Classical or Newtonian Mechanics defines Work done as in a purely mechanical way. (a mechanical way means a macrobody having displacements). Whenever a body having a mass undergoes a displacement under the influence of a force on it, classical mechanics says a work done is there.
So if F is a force vector acting on a particle due to which the particle moves travelling a "displacement" d which is also a vector, then the total work done by the force on the particle would be "dot product" of the vectors "F" and "d". So, mathematically Workdone, W can be expressed as W=F.d and in terms of "scalar" magnitude and
W=Fd CosΦ where Φ= Angle between F and d.
THERMODYNAMIC WORK:
The Energy In Transition: Energy is a physical quantity and it can move from one system to another system, from one place to another place. How does energy crosses the boundary of a system? From where energy knows the direction of travel? Those are some questions which scientists want to deliver an elusive but convincing answer.
So, in thermodynamics, energy will flow either as radiation (heat) or as Workdone otherwise. Hence thermodynamic work has a large domain in which mechanical work is a sub domain.
TOTAL ENERGY CONTENT OF AN AMOUNT OF GAS ENCLOSED IN A VESSEL
Suppose we have an enclosed vessel, where we have kept certain amount of gas. The molecules of the gas possess energy due to the molecular vibrations of the gas molecules due to Brownian Motion. Energy, thus stored as kinetic energy of the gas molecules directly depends upon the temperature of the body. For a perfect gas the kinetic energy of the molecules, energy of a molecule directly depends upon its temperature. This energy is termed as Internal Energy. It is denoted by U. Where as internal energy per unit mass is named as Specific Internal Energy and denoted by (u) Or we can write
U=m.u where m= mass of the working substance. And if Cv is the specific heat at constant volume. Now we can write, dU = m.Cv.(dt), where as the dt is the elementary change in the temperature. But, in addition to this internal energy, there is one more type of energy. To gather all the molecules of the gas from infinity distance to enclose them at the pressure P and volume V needs workdone on the molecules, this workdone is stored in the molecules as Flow Energy and is equal to PV, hence total energy possessed by the gas molecules will be the sum of internal energy and flow work, and it is called as Enthalpy denoted by H.
INEXACT DIFFERENTIALS AND EXACT DIFFERENTIALS:
In thermodynamics, an inexact differential or imperfect differential is any quantity, particularly heat Q and work W, that are not state functions (a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state), in that their values depend on how the process is performed. The symbol ,₫ or δ (in the modern sense), which originated from the work of German mathematician Carl Gottfried Neumann in his 1875 Vorlesungen über die mechanische Theorie der Wärme, indicates that Q and W are path dependent. In terms of infinitesimal quantities, the first law of thermodynamics is thus expressed as:
where δQ and δW are inexact (path-dependent), and dU is exact (path-independent).
For an exact differential df,
An inexact differential is one whose integral is path dependent. This may be expressed mathematically for a function of two variables as
A differential dQ that is not exact is said to be integrable when there is a function 1/τ such that the new differential dQ/τ is exact. The function 1/τ is called the integrating factor, τ being the integrating denominator.
As an example, the use of the inexact differential in thermodynamics is a way to mathematically quantify functions that are not state functions and are thus path dependent. In thermodynamic calculations, the use of the symbol ΔQ for heat is a mistake, since heat is not a state function having initial and final values. It would, however, be correct to use lower case δQ in the inexact differential expression for heat. The offending Δ belongs further down in the Thermodynamics section in the equation , which should be (Baierlein, p. 10, equation 1.11, though he denotes internal energy by E in place of U).[3] Continuing with the same instance of ΔQ, for example, removing the Δ, the equation
is true for constant pressure.
Temperature; a vital characteristics of stored energy in molecules. In a sense we can say the effect of energy stored in a molecule is the temperature of the molecule. In classical thermodynamics, temperature of a gas is nothing but the average kinetic energy of a molecule. In fact thermodynamics is the subject which deals with Energy, Equilibrium, Entropy often described as the study of "EEE". "Molecular Motion" is the theme of thermodynamics.
Thermodynamics is nothing but the energy mechanics ie the movement of energy in the space and time. It is quite evident from the name of the subject. "Thermos" is heat related to temperature and "dynamics" is the motion of it. The manifestation of energy trapped within a body is nothing but the temperature.
I was an observer of nature. The smallest of smalls are the components of the nature too. I still remember the day I first time saw a thermometer, I was badly attacked by viral fever. I remember my aunt told me to clasp a thin pipe of glass, with a glittering substance inside sandwiched by inner side of my left arm and the arm pit. When I asked about the object I was told that it was an instrument, that the instrument measures the magnitude of hotness or coldness and named as "thermometer".
The question that immediately popped up in my mind is that how does it measure the hotness of any object. I asked my teachers at the school, but nothing new had come out, but one thing was common in their reply to my queries and it was that whenever we place an object inside a fire, the object becomes hotter and hotter as temperature would rise and we can measure it as it would produce a rise in mercury columns.
I came to know the exact answer to my queries when I read thermodynamics in the 11th Standard. when I read about kinetic theory of gases, where temperature was defined by the average magnitude of the kinetic energy of the molecules due to their non stop & compulsory motions which was analyzed by Albert Einstein and the phenomenon is called "Brownian Motion".
When we touch a hot body, we feel the temperature as the molecules would transfer kinetic energy to my finger and the energy was converted into heat energy. So "Temperature" of a body is a macroscopic property of the body as a manifestation of energy contained in the whole body and which arises due to continuous bombardment of molecules with a high kinetic energy and transfer a portion of that energy to the body which is converted to heat.
But it must not be the complete explanation as in solids there would not be any 'Brownian Motion' unlike the molecules of a fluid, but despite this solid still have a temperature. What is the reason of this temperature? Is it still molecular kinetic energy due to which solid posses temperature?
In solid molecules are fixed at lattice points, a molecule needs a large amount of energy to make itself free from the shackles of lattice. But molecules still posses energy as it can still vibrate about its mean point ie. lattice point. This vibrational energy is responsible for solid's temperature.
These piece of article on thermodynamic concept is an earnest try to tell about energy mechanics as a story.
"Dedicated to the teaching methodology of Richard Feynman"
. . . . . . . . . . . .©sarpyl
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 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 & surroundings is called as "SYSTEM BOUNDARIES", which may be real & distinct in some cases where as some of them are virtual, but it may be real, solid and distinct.
ENERGY:
Although we can't exactly define what is Energy, yet we can say how does Energy behave, even we can measure the change in energy of the system, we may say that Energy always posses the capability to do certain amount of work depending upon the form of Energy. We can also describe the different forms of Energy those can exist like potential energy, kinetic energy, chemical energy, binding energy, nuclear energy etc.
Depending upon the capacity to do work, energy can be classified into different forms. If the energy is highly ordered then it is HIGH GRADE ENERGY, like Kinetic Energy, where as when Energy exists in a chaotic form we call it LOW GRADE ENERGY. Heat energy of a body arises due to random motions of the individual molecules. Hence we can say that HEAT ENERGY is related with the chaosness of the molecules, therefore, it is the most low grade energy.
HEAT TRANSFER :
Through the boundary, a system and its surroundings can exchange energy between them, if allowed by the boundary properties. There are three modes of energy interaction a system and surroundings. If the boundaries are permeable to allow heat flow across it, then the energy transfer mode is called HEAT TRANSFER.
When a system absorbs heat energy from the surroundings due to the temperature difference between system and surroundings the transfer of energy is named as HEAT TRANSFER.
WORK TRANSFER :
When a system has a flexible or movable boundary then energy can be transfer by virtue of workdone. If there exists a pressure gradient between a system and its surroundings then work exchange takes place between the system and the surroundings as the flexible boundary moves to destroy the pressure gradient that exists between the system and the surroundings. So we would say the Energy Transfer due to pressure gradient is named as WORK TRANSFER.
MASS TRANSFER :
For flow process in a open system, mass transfer takes place between system & surroundings which is the third type of Energy Transfer and named as Mass Transfer. Any open system has two passages for fluid flow. Through one passage, the mass of the working substance enters into the system and aptly named as INLET, while the second passage is used by the working fluid to flow out of the system and it is named as OUTLET. So, in open system mass flow occurs across the system and this phenomenon of mass inflow and outflow from the system is named as MASS TRANSFER between a system and it's boundaries.
CONCEPTS OF MASS :
What is mass? Or we can say what is it to be a substance? Here, again we face the fundamental difficulty to define Mass accurately, although we know how it does behave, we can measure its value even, but it is really not clear what is mass made of. When Einstein equates mass in terms of energy, it defines mass as a form of energy but they are bound within the mass which again consists of elementary but composite particles named electron, proton & neutron. Proton, neutrons are made of QUARKS, which are the most fundamental particles of nature. Although Quarks are already well researched, and we know the most possible reason of the “confinement” phenomenon, still there exists a large number of physical phenomenon which can be explained using the “standard model of particle physics”.
PROPERTIES OF A SYSTEM :
A system is characterized by the values of its properties. So the most logical question that would arise here would be about properties of a system. So what is a property of a system? It has been seen that every object that exists in this Universe possesses some physical & chemical characteristics, like size, shape, mass, energy, chemical composition, colors etc. Among these various characteristics, those are related with energy directly or indirectly are called as "thermodynamic functions". There are mainly two types of thermodynamic functions, which can be better described in mathematical terms as they are physical quantity and hence are measurable. Here we shall take a little hiatus (break) to know some facts about physical quantity.
Physical characteristics are of two types. Any physical characteristics can be represented by the mathematical quantity and it is thus represented by mathematical functions. There may be two types of mathematical functions. When expressed in differential form, some of the functions become Exact differential and some of them produces In-exact differential form. The exact differential functions are called as thermodynamic properties. They are also known as “Point Functions”. Where as the in-exact differentials are called “Path Functions”
EQUILIBRIUM CONDITIONS :
Every thermodynamic function are directly or indirectly measurable and when there is no energy transfer between the system and surroundings, then the value of the functions assume a certain value by which we can specify the state or condition of a thermodynamic system. So, the values are only measurable when they are not changing over a period of time. What does it implicate that the values of the thermodynamic functions are not continuously changing. When the values are not changing it indicates a stability of the state of the system over a certain periods of time. This stability of a system implies an Equilibrium condition. Each and every equilibrium states are distinct and they are specified by the distinct value of the properties of the system at that equilibrium conditions.
CONCEPTS OF A THERMODYNAMIC PLANE :
A thermodynamics system is a bi-variate function. It means that to specify a thermodynamic system we need to specify the values of any two properties. One can also describe a thermodynamic system has two degrees of freedom. So, mathematically, we can say that any thermodynamic system at a certain equilibrium condition can be represented as a point on a two dimensional plane. The plane thus formed plotting thermodynamic properties along X and Y axes of a Cartesian Coordinate system is known as thermodynamic plane.
A point on this plane represents a system at a thermodynamic equilibrium condition, which can be defined as a state which is time invariant when it is isolated from the surroundings. So, at equilibrium condition the values of different thermodynamic properties remain constant over a considerable amount of time.
EXTERNAL DISTURBANCES AND CHANGE OF STATE OF A SYSTEM:
We have already know that when the values of different thermodynamic properties become stable we get an equilibrium state where no values of the properties can be changed without application of any external influences. But, what happens, when an external agency tries to change the values of the properties of the system. Here, what does it mean by "external influences"? What does it mean in real life? We know from our daily life experiences that any kind of external influences can be at last reduced to any kind of force only and the use of external influences always lead to an exchange of energy between the system and the surroundings. To explain the phenomena we shall take a system at equilibrium with its surroundings. Hence, the pressure P and temperature T of both the system as well as the surroundings too. Now, to disturb the equilibrium condition of the system we must change either the pressure or the temperature of the system. Suppose we take a cylinder-piston assembly, whose temperature is T and pressure is P. Now suppose, we inject a small amount of energy very slowly into the system, can you tell, what type of change we should expect in this case.
Suppose we change the pressure from (P) to (P + dP) where (dP) is the change of pressure of the system, where as the pressure of the surroundings remains at (P). Then there exists a pressure difference of the flexible wall that separates our system from its surroundings. As a result a force will act on the flexible wall of the system, and the wall will move along the net force on it. Therefore, an amount of work done will be there due to the displacement of the boundary wall. There may be two type of cases, when (dP) is positive, the system does work on the surrounding as the volume of the system increases. As the volume increases from V to (V + dV) the pressure would drop to (P) from (P + dP). Hence due to this energy transfer from the system to surrounding again Equilibrium will be achieved.
VARIABLES IN THERMODYNAMICS
STATE AND COMPOSITION OF MATTER :
From our common sense we can say that matters are composed of mass, a fundamental form of energy. From our early experimentation with mass and nature, we could conclude a concept of mass as a continuous physical quantity, it implies that we can divide any quantity of mass, whatever small it may be. This view is essentially evolved on the basis of our macro world perception.
But within few years rapid growth of modern science shows that our perception of a continuous character of mass is an incorrect idea. Hence particle character was bestowed on mass that tells us that masses are made of tiny particles, that can independently exist in a stable condition and nicely named as molecules which are different for different materials. But it is not the fundamental particles of mass. There are more to come!
So, a piece of matter is really made of very large numbers of stable molecules, which scientists conclude is made of atoms. Again atoms are composed of very tiny fundamental negatively charged particles named electrons, and the core of the atoms are called as nucleus is made of chargeless neutrons and positively charged protons.
So mass is a discontinuous physical quantity and microscopic by nature! But our common perception says that it is a continuum and hence macroscopic by nature. Accordingly, there are two ways to learn thermodynamics, one is macroscopic approach, also known as Classical
Thermodynamics. and the other was named as Statistical Thermodynamics. It is basically Energy Dynamics at microscopic level.
ENERGY
The focus of Thermodynamics: As the name suggests, is primarily on energy, more specifically heat energy and related variable.(Thermos means Heat energy and Temperature).
So, first thermodynamic property is Energy itself! We use the term so frequently that we never think about its proper definition and understanding. Let me ask you one thing when someone mentions that he or she is feeling more energetic, what does he actually want to mean? In simple terms we can specify Energy as "something" that has the capacity to do work. Therefore, we can say that Energy has the capacity to do work, whatever it may be the change of anything is some way or other is connected with the exchange of Energy between bodies.
STORED ENERGY AND ENERGY IN TRANSITION :
We have defined thermodynamics as the knowledge of Energy and its movement in the space, including the dynamics of the involved mechanisms and processes. So, our prime interest would be Energy here, hence Energy must be defined as a physical quantity (hence can be measured), which has the capacity to perform useful work against any resistance.
Here, the definition of work must be given, as thermodynamic work is different from mechanical work.
MECHANICAL WORK Vs. THERMODYNAMIC WORK:
Classical or Newtonian Mechanics defines Work done as in a purely mechanical way. (a mechanical way means a macrobody having displacements). Whenever a body having a mass undergoes a displacement under the influence of a force on it, classical mechanics says a work done is there.
So if F is a force vector acting on a particle due to which the particle moves travelling a "displacement" d which is also a vector, then the total work done by the force on the particle would be "dot product" of the vectors "F" and "d". So, mathematically Workdone, W can be expressed as W=F.d and in terms of "scalar" magnitude and
W=Fd CosΦ where Φ= Angle between F and d.
THERMODYNAMIC WORK:
The Energy In Transition: Energy is a physical quantity and it can move from one system to another system, from one place to another place. How does energy crosses the boundary of a system? From where energy knows the direction of travel? Those are some questions which scientists want to deliver an elusive but convincing answer.
So, in thermodynamics, energy will flow either as radiation (heat) or as Workdone otherwise. Hence thermodynamic work has a large domain in which mechanical work is a sub domain.
TOTAL ENERGY CONTENT OF AN AMOUNT OF GAS ENCLOSED IN A VESSEL
Suppose we have an enclosed vessel, where we have kept certain amount of gas. The molecules of the gas possess energy due to the molecular vibrations of the gas molecules due to Brownian Motion. Energy, thus stored as kinetic energy of the gas molecules directly depends upon the temperature of the body. For a perfect gas the kinetic energy of the molecules, energy of a molecule directly depends upon its temperature. This energy is termed as Internal Energy. It is denoted by U. Where as internal energy per unit mass is named as Specific Internal Energy and denoted by (u) Or we can write
U=m.u where m= mass of the working substance. And if Cv is the specific heat at constant volume. Now we can write, dU = m.Cv.(dt), where as the dt is the elementary change in the temperature. But, in addition to this internal energy, there is one more type of energy. To gather all the molecules of the gas from infinity distance to enclose them at the pressure P and volume V needs workdone on the molecules, this workdone is stored in the molecules as Flow Energy and is equal to PV, hence total energy possessed by the gas molecules will be the sum of internal energy and flow work, and it is called as Enthalpy denoted by H.
H = U + PV
or
h = u + Pv (in terms of specific properties)
INEXACT DIFFERENTIALS AND EXACT DIFFERENTIALS:
In thermodynamics, an inexact differential or imperfect differential is any quantity, particularly heat Q and work W, that are not state functions (a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state), in that their values depend on how the process is performed. The symbol ,₫ or δ (in the modern sense), which originated from the work of German mathematician Carl Gottfried Neumann in his 1875 Vorlesungen über die mechanische Theorie der Wärme, indicates that Q and W are path dependent. In terms of infinitesimal quantities, the first law of thermodynamics is thus expressed as:
δQ = dU + δW
For an exact differential df,
An inexact differential is one whose integral is path dependent. This may be expressed mathematically for a function of two variables as
A differential dQ that is not exact is said to be integrable when there is a function 1/τ such that the new differential dQ/τ is exact. The function 1/τ is called the integrating factor, τ being the integrating denominator.
As an example, the use of the inexact differential in thermodynamics is a way to mathematically quantify functions that are not state functions and are thus path dependent. In thermodynamic calculations, the use of the symbol ΔQ for heat is a mistake, since heat is not a state function having initial and final values. It would, however, be correct to use lower case δQ in the inexact differential expression for heat. The offending Δ belongs further down in the Thermodynamics section in the equation , which should be (Baierlein, p. 10, equation 1.11, though he denotes internal energy by E in place of U).[3] Continuing with the same instance of ΔQ, for example, removing the Δ, the equation
is true for constant pressure.
LAWS OF THERMODYNAMICS
Thermodynamics is nothing but the energy mechanics ie the movement of energy in the space and time. It is quite evident from the name of the subject. "Thermos" is heat related to temperature and "dynamics" is the motion of it. The manifestation of energy trapped within a body is nothing but the temperature.
I was an observer of nature. The smallest of smalls are the components of the nature too. I still remember the day I first time saw a thermometer, I was badly attacked by viral fever. I remember my aunt told me to clasp a thin pipe of glass, with a glittering substance inside sandwiched by inner side of my left arm and the arm pit. When I asked about the object I was told that it was an instrument, that the instrument measures the magnitude of hotness or coldness and named as "thermometer".
The question that immediately popped up in my mind is that how does it measure the hotness of any object. I asked my teachers at the school, but nothing new had come out, but one thing was common in their reply to my queries and it was that whenever we place an object inside a fire, the object becomes hotter and hotter as temperature would rise and we can measure it as it would produce a rise in mercury columns.
I came to know the exact answer to my queries when I read thermodynamics in the 11th Standard. when I read about kinetic theory of gases, where temperature was defined by the average magnitude of the kinetic energy of the molecules due to their non stop & compulsory motions which was analyzed by Albert Einstein and the phenomenon is called "Brownian Motion".
When we touch a hot body, we feel the temperature as the molecules would transfer kinetic energy to my finger and the energy was converted into heat energy. So "Temperature" of a body is a macroscopic property of the body as a manifestation of energy contained in the whole body and which arises due to continuous bombardment of molecules with a high kinetic energy and transfer a portion of that energy to the body which is converted to heat.
But it must not be the complete explanation as in solids there would not be any 'Brownian Motion' unlike the molecules of a fluid, but despite this solid still have a temperature. What is the reason of this temperature? Is it still molecular kinetic energy due to which solid posses temperature?
In solid molecules are fixed at lattice points, a molecule needs a large amount of energy to make itself free from the shackles of lattice. But molecules still posses energy as it can still vibrate about its mean point ie. lattice point. This vibrational energy is responsible for solid's temperature.
