Lecture 2 - Need for Analysis, Additional Thermodynamics Functions, State and Path Variables

 Page 1


Thermodynamics (Classical) for Biological Systems 
Prof. G.K. Suraishkumar 
Department of Biotechnology 
Indian Institute of Technology, Madras 
 
Module No. #02 
Additional Thermodynamic Functions 
Lecture No. #02 
Need for Analysis  
Additional Thermodynamics Functions  
State and Path Variables 
 
Let us begin today by looking at the need for analysis of a biological system. As we all 
know, engineers are typically introduced to the information or the knowledge; they 
understand the knowledge toward analysis and design of the relevant system. Taking that 
view for biological engineering, we can look at getting the information first, 
understanding that, and using that to analyse and design systems of biological 
importance. To understand this a little better, let us first consider bio process industry; 
you know in the bio process industry, products of biological relevance or using 
biological systems are made for the use of mankind. 
In a biological process, it is easy to imagine or let us imagine that a liquid needs to be 
moved from one place a to another place b; typically this movement occurs through 
pipes of different sizes. And deciding on what pump to use to move the fluid from say 
point a to point b is a very important design aspect in a bioprocess. As you will learn 
later or you may have already done fluid flow courses; if you have done fluid flow 
courses, you would already know this. One of the important aspects in deciding what 
pump size to use is to know the type of flow that happens in the pipe. There are two 
major types of flows; one is the laminar flow, in which it is an ordered flow in layers, 
and the other is a turbulent flow, where pockets of fluid tumble over each other and flow 
through a pipe. 
The power requirement depends on what kind of flow we have in the pipe, to move the 
fluid from one place to another. Let us say that we do not have any information about 
whether the flow is laminar or turbulent; and let us say that we do not really know how 
Page 2


Thermodynamics (Classical) for Biological Systems 
Prof. G.K. Suraishkumar 
Department of Biotechnology 
Indian Institute of Technology, Madras 
 
Module No. #02 
Additional Thermodynamic Functions 
Lecture No. #02 
Need for Analysis  
Additional Thermodynamics Functions  
State and Path Variables 
 
Let us begin today by looking at the need for analysis of a biological system. As we all 
know, engineers are typically introduced to the information or the knowledge; they 
understand the knowledge toward analysis and design of the relevant system. Taking that 
view for biological engineering, we can look at getting the information first, 
understanding that, and using that to analyse and design systems of biological 
importance. To understand this a little better, let us first consider bio process industry; 
you know in the bio process industry, products of biological relevance or using 
biological systems are made for the use of mankind. 
In a biological process, it is easy to imagine or let us imagine that a liquid needs to be 
moved from one place a to another place b; typically this movement occurs through 
pipes of different sizes. And deciding on what pump to use to move the fluid from say 
point a to point b is a very important design aspect in a bioprocess. As you will learn 
later or you may have already done fluid flow courses; if you have done fluid flow 
courses, you would already know this. One of the important aspects in deciding what 
pump size to use is to know the type of flow that happens in the pipe. There are two 
major types of flows; one is the laminar flow, in which it is an ordered flow in layers, 
and the other is a turbulent flow, where pockets of fluid tumble over each other and flow 
through a pipe. 
The power requirement depends on what kind of flow we have in the pipe, to move the 
fluid from one place to another. Let us say that we do not have any information about 
whether the flow is laminar or turbulent; and let us say that we do not really know how 
to decide whether the flow is laminar and turbulent. The way to go about or the approach 
would be to visualize a flow in some fashion with itself it is quite difficult; you need 
transparent pipes and so on and so forth, which may not be suitable for all fluids that are 
applicable. We need to look at, what all aspects would change the type of flow involved. 
Do experiments one after another to figure out, what kind of flow exists in a particular 
piping system. We do not even know, what decides the kind of flow that happens in a 
piping system. 
Luckily for us, a lot of work has been done earlier starting from the 1900s, 1908 
Reynolds did the flow visualization experiment, where he, as a result of which, we know 
that there are four parameters that decide whether the flow is going to be laminar or 
turbulent. The four parameters are the density of the fluid, the velocity of the fluid, the 
diameter of the pipe through which the fluid is flowing, and the viscosity of the fluid. 
These four parameters decide on the nature of flow; suppose we did not know this at all, 
we did not have to do experiments one after another may be thousands of experiments to 
arrive at the same information. 
Somebody has done this, somebody has used the intuition to come up with, what you 
may already know as a Reynolds number, which is nothing but the density into velocity 
into diameter by the viscosity rho V D by mu. In a pipe flow situation, you may know 
that if the Reynolds number is less than about 2000 or 2100, the flow is going to be 
laminar, otherwise the flow is... Or above 4000 let us say, in a pipe, the flow is going to 
be turbulent. What information we could get out of thousands and thousands of 
experiments, is all compressed into this one single beautiful relationship, it is called the 
Reynolds number. And that is the advantage in analysing something, and coming up with 
a useful parameter. 
We are in the process of understanding biological systems better, and we are nowhere 
near that level of completeness in the case of a biological system. Let me present 
something else to you to understand the need for analysis, so that the design can be much 
better; and also analysis has its own benefits in terms of better and better understanding 
of the system. To do that, I am going to read out parts of a paper, this paper is titled, can 
a biologist fix a radio or what I learnt studying apoptosis. This paper is authored by a 
person called Yuri Lazebnik; he is from cold spring harbour lab, which is a very 
prestigious lab. This was published in cancer cell in 2002. I am going to read out parts of 
Page 3


Thermodynamics (Classical) for Biological Systems 
Prof. G.K. Suraishkumar 
Department of Biotechnology 
Indian Institute of Technology, Madras 
 
Module No. #02 
Additional Thermodynamic Functions 
Lecture No. #02 
Need for Analysis  
Additional Thermodynamics Functions  
State and Path Variables 
 
Let us begin today by looking at the need for analysis of a biological system. As we all 
know, engineers are typically introduced to the information or the knowledge; they 
understand the knowledge toward analysis and design of the relevant system. Taking that 
view for biological engineering, we can look at getting the information first, 
understanding that, and using that to analyse and design systems of biological 
importance. To understand this a little better, let us first consider bio process industry; 
you know in the bio process industry, products of biological relevance or using 
biological systems are made for the use of mankind. 
In a biological process, it is easy to imagine or let us imagine that a liquid needs to be 
moved from one place a to another place b; typically this movement occurs through 
pipes of different sizes. And deciding on what pump to use to move the fluid from say 
point a to point b is a very important design aspect in a bioprocess. As you will learn 
later or you may have already done fluid flow courses; if you have done fluid flow 
courses, you would already know this. One of the important aspects in deciding what 
pump size to use is to know the type of flow that happens in the pipe. There are two 
major types of flows; one is the laminar flow, in which it is an ordered flow in layers, 
and the other is a turbulent flow, where pockets of fluid tumble over each other and flow 
through a pipe. 
The power requirement depends on what kind of flow we have in the pipe, to move the 
fluid from one place to another. Let us say that we do not have any information about 
whether the flow is laminar or turbulent; and let us say that we do not really know how 
to decide whether the flow is laminar and turbulent. The way to go about or the approach 
would be to visualize a flow in some fashion with itself it is quite difficult; you need 
transparent pipes and so on and so forth, which may not be suitable for all fluids that are 
applicable. We need to look at, what all aspects would change the type of flow involved. 
Do experiments one after another to figure out, what kind of flow exists in a particular 
piping system. We do not even know, what decides the kind of flow that happens in a 
piping system. 
Luckily for us, a lot of work has been done earlier starting from the 1900s, 1908 
Reynolds did the flow visualization experiment, where he, as a result of which, we know 
that there are four parameters that decide whether the flow is going to be laminar or 
turbulent. The four parameters are the density of the fluid, the velocity of the fluid, the 
diameter of the pipe through which the fluid is flowing, and the viscosity of the fluid. 
These four parameters decide on the nature of flow; suppose we did not know this at all, 
we did not have to do experiments one after another may be thousands of experiments to 
arrive at the same information. 
Somebody has done this, somebody has used the intuition to come up with, what you 
may already know as a Reynolds number, which is nothing but the density into velocity 
into diameter by the viscosity rho V D by mu. In a pipe flow situation, you may know 
that if the Reynolds number is less than about 2000 or 2100, the flow is going to be 
laminar, otherwise the flow is... Or above 4000 let us say, in a pipe, the flow is going to 
be turbulent. What information we could get out of thousands and thousands of 
experiments, is all compressed into this one single beautiful relationship, it is called the 
Reynolds number. And that is the advantage in analysing something, and coming up with 
a useful parameter. 
We are in the process of understanding biological systems better, and we are nowhere 
near that level of completeness in the case of a biological system. Let me present 
something else to you to understand the need for analysis, so that the design can be much 
better; and also analysis has its own benefits in terms of better and better understanding 
of the system. To do that, I am going to read out parts of a paper, this paper is titled, can 
a biologist fix a radio or what I learnt studying apoptosis. This paper is authored by a 
person called Yuri Lazebnik; he is from cold spring harbour lab, which is a very 
prestigious lab. This was published in cancer cell in 2002. I am going to read out parts of 
a paper. 
Yuri Lazebnik considers the transistor radio, something that existed a long time ago, but 
I guess, he relates to that a lot better. He considers a transistor radio to be equivalent to 
the cell. The particular aspect that he is going to consider is an old broken transistor 
radio. And the objective here is to fix the radio or to repair the radio, so that it functions 
properly. Therefore, we can consider this radio to be equivalent to a human being or a 
cell to begin with; something is wrong, and we need to fix it, so that it functions 
properly. 
Reading from this paper, some parts of it; conceptually a radio functions similarly to a 
signal transaction path way in a cell, in that both convert a signal from one form to into 
another. A radio converts electromagnetic waves into sound waves. The radio has about 
a 100 various components such as resistors, capacitors and transistors, which is 
comparable to the number of molecules in a reasonably complex signal transduction 
pathway in a cell. If we take a biological way of looking at things right now, the way a 
biologist would look at it; he gives the some of the ways, in which a biologist would 
approach this problem. 
Biologist as I am talking of a classical experimental biologist, and I am sure a lot of 
people work in interdisciplinary areas now, but a classical biologist would will approach 
it a certain way. And eventually all the components will be catalogued; connections 
between them will be described, and the consequences of removing each component or 
their combinations will be documented. Can the information that we accumulated help us 
to repair the radio? The information itself is wonderful; it helps, it gives a lot more inside 
into what is happening, but is it good enough to repair the radio, is the question. The 
answer is, most likely no; unless there is a certain piece of luck that helps you in setting 
right the radio or the cell. 
Coming back to this paper, yet we know with near certainty that an engineer could fix 
the radio; what makes the difference? I think it is the languages that these two groups 
use. It is common knowledge that the human brain can keep track of only so many 
variables. It is also common experience that once the number of components in a system 
reaches a certain threshold understanding the system without formal analytical tools 
requires geniuses; who are so rare even outside biology. In engineering, this scarcity of 
Page 4


Thermodynamics (Classical) for Biological Systems 
Prof. G.K. Suraishkumar 
Department of Biotechnology 
Indian Institute of Technology, Madras 
 
Module No. #02 
Additional Thermodynamic Functions 
Lecture No. #02 
Need for Analysis  
Additional Thermodynamics Functions  
State and Path Variables 
 
Let us begin today by looking at the need for analysis of a biological system. As we all 
know, engineers are typically introduced to the information or the knowledge; they 
understand the knowledge toward analysis and design of the relevant system. Taking that 
view for biological engineering, we can look at getting the information first, 
understanding that, and using that to analyse and design systems of biological 
importance. To understand this a little better, let us first consider bio process industry; 
you know in the bio process industry, products of biological relevance or using 
biological systems are made for the use of mankind. 
In a biological process, it is easy to imagine or let us imagine that a liquid needs to be 
moved from one place a to another place b; typically this movement occurs through 
pipes of different sizes. And deciding on what pump to use to move the fluid from say 
point a to point b is a very important design aspect in a bioprocess. As you will learn 
later or you may have already done fluid flow courses; if you have done fluid flow 
courses, you would already know this. One of the important aspects in deciding what 
pump size to use is to know the type of flow that happens in the pipe. There are two 
major types of flows; one is the laminar flow, in which it is an ordered flow in layers, 
and the other is a turbulent flow, where pockets of fluid tumble over each other and flow 
through a pipe. 
The power requirement depends on what kind of flow we have in the pipe, to move the 
fluid from one place to another. Let us say that we do not have any information about 
whether the flow is laminar or turbulent; and let us say that we do not really know how 
to decide whether the flow is laminar and turbulent. The way to go about or the approach 
would be to visualize a flow in some fashion with itself it is quite difficult; you need 
transparent pipes and so on and so forth, which may not be suitable for all fluids that are 
applicable. We need to look at, what all aspects would change the type of flow involved. 
Do experiments one after another to figure out, what kind of flow exists in a particular 
piping system. We do not even know, what decides the kind of flow that happens in a 
piping system. 
Luckily for us, a lot of work has been done earlier starting from the 1900s, 1908 
Reynolds did the flow visualization experiment, where he, as a result of which, we know 
that there are four parameters that decide whether the flow is going to be laminar or 
turbulent. The four parameters are the density of the fluid, the velocity of the fluid, the 
diameter of the pipe through which the fluid is flowing, and the viscosity of the fluid. 
These four parameters decide on the nature of flow; suppose we did not know this at all, 
we did not have to do experiments one after another may be thousands of experiments to 
arrive at the same information. 
Somebody has done this, somebody has used the intuition to come up with, what you 
may already know as a Reynolds number, which is nothing but the density into velocity 
into diameter by the viscosity rho V D by mu. In a pipe flow situation, you may know 
that if the Reynolds number is less than about 2000 or 2100, the flow is going to be 
laminar, otherwise the flow is... Or above 4000 let us say, in a pipe, the flow is going to 
be turbulent. What information we could get out of thousands and thousands of 
experiments, is all compressed into this one single beautiful relationship, it is called the 
Reynolds number. And that is the advantage in analysing something, and coming up with 
a useful parameter. 
We are in the process of understanding biological systems better, and we are nowhere 
near that level of completeness in the case of a biological system. Let me present 
something else to you to understand the need for analysis, so that the design can be much 
better; and also analysis has its own benefits in terms of better and better understanding 
of the system. To do that, I am going to read out parts of a paper, this paper is titled, can 
a biologist fix a radio or what I learnt studying apoptosis. This paper is authored by a 
person called Yuri Lazebnik; he is from cold spring harbour lab, which is a very 
prestigious lab. This was published in cancer cell in 2002. I am going to read out parts of 
a paper. 
Yuri Lazebnik considers the transistor radio, something that existed a long time ago, but 
I guess, he relates to that a lot better. He considers a transistor radio to be equivalent to 
the cell. The particular aspect that he is going to consider is an old broken transistor 
radio. And the objective here is to fix the radio or to repair the radio, so that it functions 
properly. Therefore, we can consider this radio to be equivalent to a human being or a 
cell to begin with; something is wrong, and we need to fix it, so that it functions 
properly. 
Reading from this paper, some parts of it; conceptually a radio functions similarly to a 
signal transaction path way in a cell, in that both convert a signal from one form to into 
another. A radio converts electromagnetic waves into sound waves. The radio has about 
a 100 various components such as resistors, capacitors and transistors, which is 
comparable to the number of molecules in a reasonably complex signal transduction 
pathway in a cell. If we take a biological way of looking at things right now, the way a 
biologist would look at it; he gives the some of the ways, in which a biologist would 
approach this problem. 
Biologist as I am talking of a classical experimental biologist, and I am sure a lot of 
people work in interdisciplinary areas now, but a classical biologist would will approach 
it a certain way. And eventually all the components will be catalogued; connections 
between them will be described, and the consequences of removing each component or 
their combinations will be documented. Can the information that we accumulated help us 
to repair the radio? The information itself is wonderful; it helps, it gives a lot more inside 
into what is happening, but is it good enough to repair the radio, is the question. The 
answer is, most likely no; unless there is a certain piece of luck that helps you in setting 
right the radio or the cell. 
Coming back to this paper, yet we know with near certainty that an engineer could fix 
the radio; what makes the difference? I think it is the languages that these two groups 
use. It is common knowledge that the human brain can keep track of only so many 
variables. It is also common experience that once the number of components in a system 
reaches a certain threshold understanding the system without formal analytical tools 
requires geniuses; who are so rare even outside biology. In engineering, this scarcity of 
geniuses is compensated at least in part by a formal language that successfully unites the 
efforts of many individuals; that is achieving the desired effect. 
Very nicely put here; let me read it again. In engineering, the scarcity of geniuses is 
compensated, at least in part by a formal language that successfully unites the efforts of 
many individuals, thus achieving a desired effect. The language that is relevant is 
mathematics; and the tools that are relevant for understanding the systems, as we are 
going to look at are thermo dynamics, may be transport aspects, fluxes and forces and so 
on, and other relevant things. In this course, we will off course look at one aspect of 
thermodynamics, which can be used to analyse biological systems. When we finished up 
in the last class, we had reviewed some of the principles that we already knew some of 
the concepts that we already knew in thermodynamics, from your earlier classes may be 
in your school or in the first year of engineering. 
And we are going to take things further here. And one of the important things that we 
considered was classical thermodynamics verses statistical thermodynamics. We said 
that classical thermodynamics is very good to apply in the continuum regime, where 
individual molecules are not really important; whereas statistical thermodynamics is a lot 
more complete, and it gains better relevance, when it is applied to non continuum 
systems. With that, let us move forward here. Let us begin module 2; module 2, we will 
look at additional useful thermodynamic functions. 
(Refer Slide Time: 11:28) 
 
Page 5


Thermodynamics (Classical) for Biological Systems 
Prof. G.K. Suraishkumar 
Department of Biotechnology 
Indian Institute of Technology, Madras 
 
Module No. #02 
Additional Thermodynamic Functions 
Lecture No. #02 
Need for Analysis  
Additional Thermodynamics Functions  
State and Path Variables 
 
Let us begin today by looking at the need for analysis of a biological system. As we all 
know, engineers are typically introduced to the information or the knowledge; they 
understand the knowledge toward analysis and design of the relevant system. Taking that 
view for biological engineering, we can look at getting the information first, 
understanding that, and using that to analyse and design systems of biological 
importance. To understand this a little better, let us first consider bio process industry; 
you know in the bio process industry, products of biological relevance or using 
biological systems are made for the use of mankind. 
In a biological process, it is easy to imagine or let us imagine that a liquid needs to be 
moved from one place a to another place b; typically this movement occurs through 
pipes of different sizes. And deciding on what pump to use to move the fluid from say 
point a to point b is a very important design aspect in a bioprocess. As you will learn 
later or you may have already done fluid flow courses; if you have done fluid flow 
courses, you would already know this. One of the important aspects in deciding what 
pump size to use is to know the type of flow that happens in the pipe. There are two 
major types of flows; one is the laminar flow, in which it is an ordered flow in layers, 
and the other is a turbulent flow, where pockets of fluid tumble over each other and flow 
through a pipe. 
The power requirement depends on what kind of flow we have in the pipe, to move the 
fluid from one place to another. Let us say that we do not have any information about 
whether the flow is laminar or turbulent; and let us say that we do not really know how 
to decide whether the flow is laminar and turbulent. The way to go about or the approach 
would be to visualize a flow in some fashion with itself it is quite difficult; you need 
transparent pipes and so on and so forth, which may not be suitable for all fluids that are 
applicable. We need to look at, what all aspects would change the type of flow involved. 
Do experiments one after another to figure out, what kind of flow exists in a particular 
piping system. We do not even know, what decides the kind of flow that happens in a 
piping system. 
Luckily for us, a lot of work has been done earlier starting from the 1900s, 1908 
Reynolds did the flow visualization experiment, where he, as a result of which, we know 
that there are four parameters that decide whether the flow is going to be laminar or 
turbulent. The four parameters are the density of the fluid, the velocity of the fluid, the 
diameter of the pipe through which the fluid is flowing, and the viscosity of the fluid. 
These four parameters decide on the nature of flow; suppose we did not know this at all, 
we did not have to do experiments one after another may be thousands of experiments to 
arrive at the same information. 
Somebody has done this, somebody has used the intuition to come up with, what you 
may already know as a Reynolds number, which is nothing but the density into velocity 
into diameter by the viscosity rho V D by mu. In a pipe flow situation, you may know 
that if the Reynolds number is less than about 2000 or 2100, the flow is going to be 
laminar, otherwise the flow is... Or above 4000 let us say, in a pipe, the flow is going to 
be turbulent. What information we could get out of thousands and thousands of 
experiments, is all compressed into this one single beautiful relationship, it is called the 
Reynolds number. And that is the advantage in analysing something, and coming up with 
a useful parameter. 
We are in the process of understanding biological systems better, and we are nowhere 
near that level of completeness in the case of a biological system. Let me present 
something else to you to understand the need for analysis, so that the design can be much 
better; and also analysis has its own benefits in terms of better and better understanding 
of the system. To do that, I am going to read out parts of a paper, this paper is titled, can 
a biologist fix a radio or what I learnt studying apoptosis. This paper is authored by a 
person called Yuri Lazebnik; he is from cold spring harbour lab, which is a very 
prestigious lab. This was published in cancer cell in 2002. I am going to read out parts of 
a paper. 
Yuri Lazebnik considers the transistor radio, something that existed a long time ago, but 
I guess, he relates to that a lot better. He considers a transistor radio to be equivalent to 
the cell. The particular aspect that he is going to consider is an old broken transistor 
radio. And the objective here is to fix the radio or to repair the radio, so that it functions 
properly. Therefore, we can consider this radio to be equivalent to a human being or a 
cell to begin with; something is wrong, and we need to fix it, so that it functions 
properly. 
Reading from this paper, some parts of it; conceptually a radio functions similarly to a 
signal transaction path way in a cell, in that both convert a signal from one form to into 
another. A radio converts electromagnetic waves into sound waves. The radio has about 
a 100 various components such as resistors, capacitors and transistors, which is 
comparable to the number of molecules in a reasonably complex signal transduction 
pathway in a cell. If we take a biological way of looking at things right now, the way a 
biologist would look at it; he gives the some of the ways, in which a biologist would 
approach this problem. 
Biologist as I am talking of a classical experimental biologist, and I am sure a lot of 
people work in interdisciplinary areas now, but a classical biologist would will approach 
it a certain way. And eventually all the components will be catalogued; connections 
between them will be described, and the consequences of removing each component or 
their combinations will be documented. Can the information that we accumulated help us 
to repair the radio? The information itself is wonderful; it helps, it gives a lot more inside 
into what is happening, but is it good enough to repair the radio, is the question. The 
answer is, most likely no; unless there is a certain piece of luck that helps you in setting 
right the radio or the cell. 
Coming back to this paper, yet we know with near certainty that an engineer could fix 
the radio; what makes the difference? I think it is the languages that these two groups 
use. It is common knowledge that the human brain can keep track of only so many 
variables. It is also common experience that once the number of components in a system 
reaches a certain threshold understanding the system without formal analytical tools 
requires geniuses; who are so rare even outside biology. In engineering, this scarcity of 
geniuses is compensated at least in part by a formal language that successfully unites the 
efforts of many individuals; that is achieving the desired effect. 
Very nicely put here; let me read it again. In engineering, the scarcity of geniuses is 
compensated, at least in part by a formal language that successfully unites the efforts of 
many individuals, thus achieving a desired effect. The language that is relevant is 
mathematics; and the tools that are relevant for understanding the systems, as we are 
going to look at are thermo dynamics, may be transport aspects, fluxes and forces and so 
on, and other relevant things. In this course, we will off course look at one aspect of 
thermodynamics, which can be used to analyse biological systems. When we finished up 
in the last class, we had reviewed some of the principles that we already knew some of 
the concepts that we already knew in thermodynamics, from your earlier classes may be 
in your school or in the first year of engineering. 
And we are going to take things further here. And one of the important things that we 
considered was classical thermodynamics verses statistical thermodynamics. We said 
that classical thermodynamics is very good to apply in the continuum regime, where 
individual molecules are not really important; whereas statistical thermodynamics is a lot 
more complete, and it gains better relevance, when it is applied to non continuum 
systems. With that, let us move forward here. Let us begin module 2; module 2, we will 
look at additional useful thermodynamic functions. 
(Refer Slide Time: 11:28) 
 
We also saw during the review that the consequences of the 0
th
 law if you if you recall 
what 0
th
 law was f x is an thermal equilibrium with z, y another body in thermal 
equilibrium with z, then separately they are in thermal equilibrium with z, then they are 
in thermal equilibrium with each other. And what came out as a consequence of the 0
th
 
law, was temperature. What came out of the first law, which essentially related the 
energy, that energies, that cross the system boundaries to the energy changes that happen 
inside the system; that give rise to the first law. And the consequence of the first law was 
the thermodynamic property called internal energy, which is represented by the symbol 
U. 
The consequence of the second law, which essentially gave us a means for the 
directionality of the process is, what we saw in the review was the thermodynamic 
quantity entropy, which is represented by the letter S. These three thermodynamics 
properties T, U and S along with pressure and volume or specific volume are actually 
sufficient to describe the thermodynamics or thermodynamics relationship of any system. 
Nevertheless for ease of use in certain applications, say processes at constant temperature 
or at constant pressure or at constant specific volume and so on and so forth. We could 
derive certain other thermodynamics variables that will turn out be easier to use. And let 
us define some other, some such thermodynamic properties next. 
(Refer Slide Time: 13:46) 
 
The first thermodynamic property that we are going to additional thermodynamic