Third law of Thermodynamics and concepts of entropy

1. Concepts of Entropy &
Third law of Thermodynamics

2. CLAUSIUS INEQUALITY
• The Clausius theorem states that a thermodynamic system
(e.g. heat engine or heat pump) exchanging heat with external
reservoirs and undergoing a thermodynamic cycle,
• where is the infinitesimal amount of heat absorbed by the
system from the reservoir and is the temperature of the
external reservoir (surroundings) at a particular instant in
time. The closed integral is carried out along
a thermodynamic process path from the initial/final state to
the same initial/final state. In principal, the closed integral can
start and end at an arbitrary point along the path.
• If there are multiple reservoirs with different
temperatures then Clausius inequality reads:

3. • In the special case of a reversible process, the equality
holds.The reversible case is used to introduce the state
function known as entropy. This is because in a cyclic
process the variation of a state function is zero. In
other words, the Clausius statement states that it is
impossible to construct a device whose sole effect is
the transfer of heat from a cool reservoir to a hot
reservoir. Equivalently, heat spontaneously flows from
a hot body to a cooler one, not the other way around.
• The generalized "inequality of Clausius“
for an infinitesimal change in entropy S applies not only
to cyclic processes, but to any process that occurs in a
closed system.

4. Concept of Entropy
• “Entropy is a function of a quantity of heat
which shows the possibility of conversion of
that heat into work. The increase in entropy is
small when heat is added at a high
temperature and is greater when heat
addition is made at a lower temperature. Thus
for maximum entropy, there is minimum
availability for conversion into work and for
minimum entropy there is maximum
availability for conversion into work.”

5. Entropy Change During
Thermodynamic Process
• Let m Kg of gas at a pressure P1, volume V1 ,
absolute temperature T1 and entropy S1, be
heated by any thermodynamic process.
• Its final pressure, volume, temperature and
entropy are P2 , V2 , T2 and S2 respectively.

6. Law Of Conservation Of Energy
• δ Q = dU + W,
Where,
• δQ = small change in heat
• dU = small change in internal energy
• δW = small change of work done
• dT = small change in temperature
• dv = small change in volume
• δQ = mC dT + pdv

7. Dividing the equation by T

8. Substituting the

10. Entropy Change For Pure Substances
• Consider (M) Kg of ice is heated continuously
at constant atmospheric pressure.

11. • T₁ = initial temperature of ice
• T₂ = melting temperature of ice = 0C = 273 K
• T = boiling temperature of water =100C
• Tᵤ = superheated steam temperature Cᵨᵢ =
specific heat of ice
• Cᵨᵥᵥ = specific heat of water
• Cᵨ = specific heat of steam

12. Process 1-2 Sensible Heating Of Ice
• Temperature of ice increase from T to ₁ T .
Change of entropy during 1-2

13. Process 2-3 Melting Of Ice
• On further heating of ice is converted into
water at constant temperature T ₂ (0C).
• The heat supplied is utilized to change phase
called latent heat of fusion of ice (h ). ᵢ
• Therefore Q = mhᵢ
• Change of entropy during process

14. Process 3-4 Sensible Heating Of Water
• Water from T is heated to water at T ₂ .
• Change of entropy during process

15. Process 4-5 Boiling Of Water
• On further heating of water, is converted into
steam at constant temperature T .
• The heat supplied is utilized to change phase
called latent heat of evaporation.
• Change of entropy during process.

16. Process 5-6 Sensible Heating Of Steam
• Temperature of steam increases from Ts to
Tsup

17. T ds Equations
• The differential form of the conservation of energy
equation for a closed stationary system (a fixed
mass) containing a simple compressible substance
can be expressed for an internally reversible process
as

18. • This equation is known as the first T ds, or Gibbs, equation.
Notice that the only type of work interaction a simple
compressible system may involve as it undergoes an internally
reversible process is the boundary work. The second T ds
equation is obtained by eliminating du from Eq. 7–23 by using
the definition of enthalpy (h u Pv):
• These T ds relations are developed with an internally
reversible process in mind since the entropy change between
two states must be evaluated along a reversible path.
However, the results obtained are valid for both reversible
and irreversible processes since entropy is a property and the
change in a property between two states is independent of
the type of process the system undergoes.

19. • Explicit relations for differential changes in
entropy are obtained by solving for ds in Eqs:-

20. Third law of Thermodynamics
• The third law of thermodynamics is stated as
follow :
‘‘The entropy of all perfect crystalline
solids is zero at absolute zero temperature’’.
• The third law of thermodynamics, often
referred to as Nernst Law, provides the basis
for the calculation of absolute entropies of
substances.

21. • According to this law, if the entropy is zero at T
= 0, the absolute entropy sab. of a substance
at any temperature T and pressure p is
expressed by the expression.

22. • Thus by putting s = 0 at T = 0, one may integrate
zero kelvin and standard state of 278.15 K and 1
atm., and find the entropy difference. Further, it
can be shown that the entropy of a crystalline
substance at T = 0 is not a function of pressure,
viz.
• However, at temperatures above absolute zero,
the entropy is a function of pressure also. The
absolute entropy of a substance at 1 atm
pressure can be calculated using eqn; for
pressures different from 1 atm, necessary
corrections have to be applied.

23. Application
• Provides an absolute reference point for the
determination of entropy.
• Explaining the behaviour of solids at very low
temperature.
• Measurement of action of chemical forces of
the reacting substances.
• Analysing the chemical and phase
equilibrium.