Concepts of Thermodynamics
Prof. Suman Chakraborty Department of Mechanical Engineering
Indian Institute of Technology, Kharagpur
Lecture - 36
Factors for Irreversibility and Introduction to Reversible Cycles In the previous lecture, we were discussing
about a Reversible process. But from the one example of reversible process that I put forward,
you can clearly understand that reversible process is such a process which is so hypothetical
that it might not actually occur in practice because of the extreme slowness of the process.
So, in practice there are Omni present factors that can make a process irreversible. So,
let me identify some of the factors which can make a process irreversible. Friction; why I start with friction is because
I have already given an example, why friction can make a process irreversible. Free or unrestrained
expansion, mixing, non mechanical origin like Hysteresis, eddy current loss etcetera and something very special which is little
bit different from these categories, which I will write with a different color. Heat
transfer across a finite temperature difference. So, why this is of a different category? I
will come to this in a moment. So, friction we have already discussed. We will come to
free expansion. So, let us take an example, where you have a chamber. On one side there
is gas and another side there is vacuum. There is a thin membrane that separates these two.
Suddenly, you puncture this membrane. Once you puncture this membrane, the gas fills
up the entire space. So, this is called as free expansion because here there was vacuum
there is no resistance against the expansion of this gas. Now, let us say you want to reverse
this process. So, what you have to do? Now you have to put a compressor so that the volume
of the gas is compressed up to this and then, put a chamber here and vacuum will be created
here. So, to compress the gas from this total volume
to this volume, this is not a spontaneous process. So, you have to put some external
work for it and when you put some external work for it. This gas will be more energized.
So, it will be hotter as compared to the state at which it started. So, to bring it back
to the same original state you have to transfer some heat to the surroundings. In the process
the gas may come back to the original state, but the surroundings are no more back to the
same state because of a net heat transfer to the surroundings. The next point is mixing
and mixing is very much like free expansion, where here instead of gas and vacuum it is
say gas 1 and gas 2. So, when you have gas 1 and gas 2 and you
remove the partition, they will spontaneously mix this does not require any work input.
But to separate these two gases again, you require some work input like something like
you know the Maxwell’s demon type of thing that I talked about hypothetically in the
previous class. So, you require some energy you know to have
a separation between gas 1 and gas 2. For example, in as a mechanical device often to
separate a high density fluid from a low density fluid, we use a rotating device called a centrifuge.
So, it creates a rotational force centrifugal force that separates the heavier fluid from
a denser fluid. So, you require a some kind of external work to separate these two, but
to make this you do not require any work that is the difference. Hysteresis and eddy current
losses are like friction in electrical and magnetic systems. So, their role in creating
an irreversibility is like friction. So, all these factors which can make a process
irreversible and you can see that they are very commonly present like can you imagine
a device without friction; you cannot. Without friction there is no real life situation.
So, all real life processes are irreversible. So, then one important point is that when
you are talking about these ones, they have a special significance. What is the special
significance? Special significance is that the source of irreversibility is within the
system itself. And therefore, this is called as internal
irreversibility. When we talk about heat transfer, heat transfer is always you know some heat
exchange between system and surrounding. So, it is not so only involving the system, it
also involves the surrounding. So, heat transfer across a finite temperature difference is
something that can make a process irreversible. We will first understand why and then, we
will put it in for a different category which is external irreversibility. So, first why
heat transfer across a finite temperature difference is irreversible? So, let us say
that this is that heat source at temperature T H greater than T L.
So, if you put these two bodies in thermal contact spontaneously there will be a heat
transfer from the high temperature to a low temperature body. This is spontaneous. Now
if you want to bring this heat Q back from here to here that is not spontaneous; so,
to do that you have to have an arrangement. What is the arrangement? The arrangement is
you have to put a device which will have work input and then, only in a cycle you have heat
transfer may be the same heat transferred back from these two. So, when you have this
same heat transfer here back, you are also adding a net work to the system.
So, when you are adding a network to the system, the system now has more energy as compared
to the state at which you know it was there when there was a spontaneous heat transfer
from here to here. So, to release that energy so that the system comes back to its original
state, what you have to do? You have to get rid of this heat, this work, this energy that
you have put through heat transfer. If you do that, the system will come back to its
original state, but the surroundings will not come back to the original state.
So, moral of the story is that because this work input is required to reverse the process
that will impart additional energy to the system to bring it back to the original state,
you have to release that energy through heat transfer to the surroundings. How much is
that energy? That energy depends on the temperature difference between T H and T L. So, if T H
and T L are very close, then this energy input is very little and then it is almost reversible.
So, what we can understand from here is that if you transfer heat across a very small temperature
difference, then actually you are almost approaching a reversible heat transfer. But the problem
is this is not practical; why? The heat transfer rate Q dot is proportional to the areas across
which heat transfer is taking place and it is proportional to coefficient and it is;
I am not let us not come to the coefficient because I still keep it proportional and it
is proportional to delta T. The proportionality is replaced with an equality with a coefficient
called as heat transfer coefficient. I am not coming into that. So, my point is that
the heat transfer rate is proportional to area of for heat transfer and it is proportional
to delta T. So, what it means is that if delta T is tending
to 0 for finite heat transfer, this must tend to infinity right. So, you must have say an
infinitely large surface area of a boiler to have a reversible heat transfer. So, that
is something that may not be possible. Practical engineering constraint is that you have a
limited area over which you can build up your heat transfer devices; limited surface area.
So, all the practical heat transfer processes are irreversible. So, this being a source
of irreversibility external to the system; you can imagine this as a system. So, external
to the system because heat transfer is taking place external to the system this is called
as externally reversible. So, quasi equilibrium process
will ensure internal reversibility, but it does not ensure external irreversibility;
external reversibility. For example, let me give you one example. So, you have a cylinder
in which you have a piston. This piston moves very slowly with you knows successive addition
or removal of this weight. But it is exchanging heat with a reservoir T H and here the temperature
is T and T H is greater than T. So, this heat transfer we will make the process
undertaken by the fluid between the piston and the cylinder effectively irreversible;
although it is internally reversible which is due to quasi equilibrium nature of the
process, but it is externally irreversible and because it is externally irreversible
either externally or internally reversible means the net process will be reversible.
In thermodynamics, there are certain types of processes where certain physical and mathematical
inferences can be drawn for which it is sufficient that the process is internally reversible;
externally irreversibility is not into purview while developing those theories and those
are called as internally reversible or endo reversible processes; either internally reversible
or endo reversible processes, where external irreversibility is not under the purview.
It is the internal reversibility that is what is ensured.
So, with this basic understanding of reversible processes, we will imagine. So, reversible
is something which is ideal right. So, we will imagine; now, a cycle which comprises
only reversible processes. So, example of a reversible cycle.
Internally as well as externally? Internally as well as externally. This is
a complete reversible cycle. So, let us say that you have a piston cylinder arrangement.
You compress this very slowly, slow compression; some gas is there and you insulate this. So,
if it is slow and you insulate this; so, there is no question of external irreversibility
because heat transfer is 0. So, it is adiabatic and it is slow. So, quasi equilibrium is assured.
So, it is internally reversible plus externally reversible. So, we can say that this is reversible
plus adiabatic compression. Next what we do is that the same piston cylinder.
Now, we take away the insulation, before that let me tell you a very interesting thing.
When I was a school student, the way in which adiabatic process was explained to me was
something like this. That adiabatic process is such a fast process, where there is insufficient
time for heat transfer. So, that you know effectively the heat transfer during the process
can be neglected. So, that is definitely true as an example of an adiabatic process. But
you can achieve adiabatic process in many ways. So, sometimes that first level of information
that you gather from school level study it becomes so emphatic that you lose the perception
that well that is true, but that is just an example.
Another example of reversible process; another example of adiabatic process could be that
you instead of very fast, you can have something very slow; diametrically opposite, but you
put an insulation around the cylinder. So, that there is no heat transfer ok. Then, next
is you take away this insulation and transfer some heat from this heat source reversibly
to this allowing it to slowly expand. So, to have reversible process, what kind of heat
transfer you should have? You should have heat transfer with minimal temperature difference
between these two. So, infinitesimal; so these temperature at the system boundary will be
say T H minus d T H. In books we normally do not write d T H because
this is differentially small, but conceptually this is if this is T H this is T H minus d
T H. If both are T H you cannot have heat transfer because heat transfer requires a
temperature difference. So, with this and the temperature of the entire system during
this slow expansion remains constant which is T H minus d T H. So, for all practical
purposes d T T H, this is reversible isothermal heat addition
and in this process, it will expand right. If you heat, it will expand in a reversible
adiabatic process. So, this is the expansion. Then, we put back the insulation again
and keep on expanding it slowly. So, this is reversible adiabatic expansion. So, after
all these expansion; so all these are reversible processes. After all this expansion, you know
the gas in terms of pressure volume temperature is not at the same initial state. So, to bring
it back to the initial state you require another process and that process has to be heat rejection.
So, that so that you know it can get compressed and come back to the original state.
So, in this process, it will reject heat. So, if this is T L. So, this is Q H. If this
is Q L, then this what is this temperature? This is T L plus d T L. So, this is reversible
plus isothermal heat rejection; reversible plus isothermal heat rejection. So, you have
a cycle in which the fluid operates between two temperature limits and does a net work.
So, it satisfies the Kelvin Planck statement. Essentially the cycle has 2 reversible adiabatic
processes and 2 reversible isothermal processes. So, this kind of cycle, where all the processes
are reversible is a reversible cycle and there could be different reversible cycles. This
is an example of a reversible cycle; when two of the processes are reversible adiabatic
and two of the processes are reversible isothermal. This cycle is called as the Carnot Cycle.
Keep one thing in mind Carnot cycle is not the only reversible cycle in the world. So,
this is just an example of a reversible cycle, but there could be several other reversible
cycles all hypothetical, but still possible where all the processes comprising the cycle
are reversible. Carnot cycle is a special example of a reversible cycle, where two processes
are reversible adiabatic and two processes are reversible isothermal and these 4 processes
comprise a cycle. Now, I started with an example of a Carnot
Cycle with an understanding that you know this gives you transition from school level
understanding to you know more advanced understanding in concepts of thermodynamics. But in practice
there could be other examples, where Carnot cycle could be a cycle involving a flow process
instead of a control mass system. Here, the substance undergoing the cycle is a control
mass system. So, I will now give you an example where the Carnot cycle can be conceptualized
for a flow process. A hypothetical power plant based on Carnot cycle. So, to understand that see we
have already through the first law of thermodynamics steady state steady flow processes what introduce
two different types of devices like boiler, turbine, condenser, compressor. So, we will
combine all those to form a cycle. So, what we will do is we will draw a diagram say you
have a Boiler at temperature T H; how do you maintain the boiler at a constant temperature
T H? Very simple, you allow the water by heating to get converted into steam. So, from water
to water vapor, it will change its phase at constant temperature because water is a simple
compressible pure substance. So, there is a heat source at T H. So, the
there will be a heat transfer to the boiler. So, this is T H minus d T H; then from the
boiler, fluid enters the turbine that fluid undergoes. So, this is reversible plus isothermal,
then the fluid undergoes are reversible and adiabatic expansion in a turbine and there
ia work output. So, this is reversible plus adiabatic, then the fluid enters the condenser
and it rejects heat so that you know steam condenses and typically there is a river,
water to which it rejects heat. So, if this temperature is T L. This is if this is T L;
this is T L plus d T L. So, this is condenser and then, now the fluid
is at a lower pressure because after expansion in the turbine the pressure has reduced. So,
it requires a compression process. So, this is compressor which requires. So, I will not
write W net here; I will write W turbine which is the work output and there is a work input
which is the compressor work. So, the net work is W turbine minus W compressor that
you get from the cycle and then it is back to the boiler. So, this is reversible plus
isothermal. This is reversible plus adiabatic compression.
So, what we can gather from this example is that this is a flow process right. So, this
is not a control mass system undergoing any process, but still out of the 4 components
which constitute this cycle, you have two processes which are taking place at reversible
isothermal condition and two processes at reversible adiabatic condition. So, by definition
this is also a Carnot cycle. Now so far so good, but we will see later
on that why practically it is impossible to set up such a cycle in a thermal power plant.
When we will study the thermal power plant cycles towards the end of this course, we
will revisit that, but you know even though we cannot practically construct this; this
remains like a benchmark. So, that you can compare the performances of various cycles;
practical cycles with respect to this ideal, but still very hypothetical.
We come to a conclusion of today’s discussion here and in the next lecture, we will learn
two things; one is what are the constraints governing the efficiencies of reversible and
irreversible cycles operating between two given temperature limits and number 2, based
on that how we can construct an absolute temperature scale independent of the properties of a thermometric
substance. These two things we will take up in the next lecture.
Thank you very much.
