second law of thermodynamics

1. M Sc Engineering in Energy Systems
Planning and Management
I/I
THERMO-FLUID
ENGINEERING
Second Law of Thermodynamics

2. Why Second Law of Thermodynamics?
First law of thermodynamics explains thermodynamic processes
with reference to mass conservation and energy conservation.
It deals with the quantitative aspect of the energy and gives the
only condition that any process is possible provided that the total
energy remains constant.
But some processes in nature cannot occur although energy
conservation principle is satisfied.
In this regard, second law of thermodynamics deals with quality or
nature of energy and defines the direction of the process in which
the system can proceed.
THERMO-FLUID ENGINEERING

3. Example 1
According the first law of thermodynamics, for a cyclic process net
heat transfer is equal to net work transfer.
But any real device, even operating on a cycle, cannot convert heat
supplied to it completely into output work.
Hence, the second law of thermodynamics explains why any real
engine cannot operate without heat loss.
Example 2
THERMO-FLUID ENGINEERING

4. Example 3
Work always produces some heat itself. But the reverse process i.e.,
the self conversion of heat to work (without any device) cannot
occur.
The second and third examples discussed above present the basic
nature or inherent tendency of a system (or a process); that most of
the processes in nature proceed in only direction. Such directional
feature of the processes cannot be explained only with the first law
of thermodynamics.
THERMO-FLUID ENGINEERING

5. Entropy
The main feature of the second law of thermodynamics is that it
defines the directions of the processes. Second law of
thermodynamics defines the direction of the process with reference
to the system property called entropy.
• System itself tends to undergo a process from less uncertain or
less random state to more uncertain or more random state. But
the reverse direction is not possible.
• High grade of energy (work) itself get converted into low grade
of energy (heat) and the reverse direction is not possible (without
nay device)
The property of a system which gives a measure of molecular
randomness, disorder or uncertainty existing in a system is called
entropy. It is an extensive property and is denoted by S.
THERMO-FLUID ENGINEERING

6. Second Law of Thermodynamics for an Isolated System
Entropy of an isolated system always increases or may remain
constant (in an ideal process).
Any isolated system can proceed in the direction in which its
randomness or uncertainty i.e., entropy increases.
This feature of the isolated system can be stated as the second law
of thermodynamics as
THERMO-FLUID ENGINEERING
The difference between entropies at the final state and the initial
state during any process is called entropy production or entropy
generation and is denoted by Sgen.

7. THERMO-FLUID ENGINEERING
According to second law of thermodynamics, during any real
process net entropy change is always greater than or equal to zero,
i.e, for any process between state 1 and state 2,
Reversible and Irreversible Processes
During any process if S2 = S1 ; the reverse process is also possible
because entropy is same for both forward and reverse direction.
Hence the process is called reversible process.
S2  S1
During any process, if S2 > S1, i.e., entropy increases in forward
direction, then the reverse direction is not possible because any real
process can not result in decrease in entropy. Hence the process is
called an irreversible process.
We can rewrite the above Equation in equivalent from to avoid
inequality sign as

8. THERMO-FLUID ENGINEERING
A process is said to be a reversible process if the initial conditions
of both the system and surroundings can be restored by the reverse
action such that net change in entropy is zero for both forward and
reverse process.
A process is said to be an irreversible process, if the initial
conditions of both the system and surroundings cannot be restored
(certain effects are left either on the system or on the surroundings)
by the reverse action. In this case entropy of the system increases in
forward process and therefore reverse direction is not possible.

9. THERMO-FLUID ENGINEERING
Entropy Relations
Applying state postulate, we can determine the internal energy of a
system if its volume and entropy are given as
U = U (S,V)
The change in internal energy during any process is then given as
The first partial derivative is equal to the temperature and the
second partial derivative is equal to the negative of the pressure, i.e.,
Substituting T and P in the above Equation,
……… Gibbs Equation

10. THERMO-FLUID ENGINEERING
Rearranging Gibbs equation, we can get the expression for the
change in entropy as
The control mass formulation of the second law of thermodynamics
gives the expression for the change in entropy of the control mass
because of heat transfer and work transfer.
Control Mass Formulation of Second Law of
Thermodynamics
For this formulation, we first find out the effects of heat transfer
and work transfer separately on the entropy of the control mass and
then we can develop the general expression and statement for the
second law of thermodynamics for a control mass.

11. THERMO-FLUID ENGINEERING
Contribution of Heat Transfer on Entropy
To determine the effect of heat transfer on entropy, we consider a
system having infinite heat capacity such that its temperature is
unaffected by the heat transfer. Such an idealized system which can
interact with its surroundings only by heat transfer (but not work
transfer) is called a reversible heat transfer reservoir and is
specified by its temperature Ti.

12. THERMO-FLUID ENGINEERING
Substituting W = PdV = 0 into Gibbs Equation, we get
Applying first law of thermodynamics, we get
Substituting dU into the above Equation, we get an expression for
the change in entropy due to a reversible heat transfer process as
It shows that entropy of a system increase if heat is supplied to it and
decrease if it loses heat.

13. THERMO-FLUID ENGINEERING
Contribution of Work Transfer on Entropy
To determine the effect of work transfer on entropy, we consider a
system having infinite work capacity such that its pressure is
unaffected by the work transfer. Such an idealized system which can
interact with its surroundings only by work transfer (but not heat
transfer) is called a reversible work transfer reservoir and is
specified by its pressure Pi.
Applying first law of thermodynamics for a reversible work transfer
reservoir, we get
Substituting dU into Gibbs Equation, we get an expression for the
change in entropy due to a reversible work transfer process as

14. THERMO-FLUID ENGINEERING
It shows that work transfer does not have any contribution on the
entropy of the system.
Since the total change in entropy of the isolated system is given by
the sum of the change in entropy of the control mass, the change in
entropy of the reversible heat transfer reservoirs and the change in
entropy of the reversible work transfer reservoirs, i.e.,
Control Mass Formulation
Now, applying second law of
thermodynamics for the isolated
system

15. THERMO-FLUID ENGINEERING
If (Qi)RHTRS is the heat supplied to the reservoir at temperature Ti,
that is supplied by the control mass, therefore,
The above Equation reduces to
With reference to the above Equation, second law of
thermodynamics for a control mass can be stated as,
The change in entropy of a control mass is greater than or equal
to the sum of heat transfers divided by the corresponding
boundary absolute temperatures.

16. THERMO-FLUID ENGINEERING
The above can also be expressed in terms of entropy generation to
avoid inequality sign as
The above Equations can also be expressed in terms of rate as

17. THERMO-FLUID ENGINEERING
Control Volume Formulation of Second Law of
Thermodynamics
Control volume formulation of second law of thermodynamics gives
the expression for the change of entropy of a control volume due to
mass transfer as well as energy transfer.
The effect of mass transfer on the entropy can be determined by
evaluating properties of working substance at the inlet and outlet.
The effects heat transfer and work transfer on the entropy of the
control volume is similar to that for the control mass.
Therefore, we can state the second law of thermodynamics for a
control volume as
The change in entropy of a control volume minus the net entropy
change of working substance due to mass transfer is greater
than or equal to the sum of heat transfers divided by the
corresponding boundary absolute temperatures.

18. THERMO-FLUID ENGINEERING
The above Equation can also be expressed in terms of entropy
generation to avoid inequality sign as

19. THERMO-FLUID ENGINEERING
Isentropic Efficiency of Steady Flow Devices
The process occurring in any steady flow device will be isentropic if
it does not involve any kind of losses (frictional loss, heat loss, etc)
therefore isentropic process is an ideal process.
But the process occurring in any real device involves losses and the
real process differs from the idealized isentropic condition.
The performance of the real device is compared with the idealized
device (isentropic) with reference to isentropic efficiency.
Isentropic Efficiency of a Turbine
In case of work producing device real work is always less than the
isentropic work output because of losses.
Hence, the isentropic efficiency of a turbine is defined as the ratio of
work output from a real turbine and the work that would have been
produced when the turbine operates under isentropic condition, i.e.,

20. THERMO-FLUID ENGINEERING
Isentropic Efficiency of a Pump/Compressor
In case of work consuming device real work is always more than the
isentropic work input because we have to increase work input to
overcome the losses to get the same desired output effect.
Hence, the isentropic efficiency of a pump or compressor is defined
as the ratio of the work that would have been required when the
pump/compressor operates under isentropic condition to work
required for the real pump/compressor and, i.e.,
Isentropic Efficiency of a Nozzle
Similarly, the isentropic efficiency of a nozzle is defined as the ratio
of the kinetic energy of the fluid at the real nozzle exit to the kinetic
energy value at the exit of an isentropic nozzle for the same inlet
state and exit pressure, i.e.,