Implication of Nernst's Heat Theorem and Its application to deduce III law of thermodynamics and Determination of absolute entropies of perfectly crystalline solids using III law of thermodynamics

1. Submitted to
Dr. S Sreenivasa
The Coordinator
Department of Studies and Research in Organic chemistry
Tumkur University, Tumakuru
TUMKUR UNIVERSITY
TUMAKURU
DEPARTMENT OF STUDIES AND RESEARCH IN ORGANIC CHEMISTRY
Seminar Topic:
“THIRD LAW OF THERMODYNAMICS”
Submitted By
Priyanka R H
I M.Sc. I Sem
Department of Studies and Research in Organic chemistry
Tumkur University, Tumakuru
Under the Guidance
Pruthviraj K
Department of Studies and Research in Organic chemistry
Tumkur University, Tumakuru

2. • INTRODUCTION
• THE NERNST HEAT THEOREM
• THIRD LAW OF THERMODYNAMICS
• DETERMINATION OF ABSOLUTE ENTROPIES
• RESIDUAL ENTROPY
• IMPORTANCE OF THIRD LAW OF THERMODYNAMICS
• REFERENCES
CONTENTS

3. THE THIRD LAW OF THERMODYNAMICS
Introduction:
Nernst work on heat theorem and electrochemistry has a very great impact on
the physical science. He was one of the great pioneer’s of physical chemistry. In a lecture
he delivered at oxford in 1937, he said that it had taker three people to formulate the first
law of thermodynamics, two for the second law, but that he had been obliged to do the third
law all by himself. He added that it followed by extrapolation that there could never be a
fourth law.
Walther Nernst (1864-1941), the German chemist was a awarded the 1920
chemistry noble prize for this work in thermochemistry.
The first and second laws of thermodynamics have led to new concepts of energy
content and entropy. The third law however does not lead to any new concept. It only places
a limitations of the value of the entropy of a crystalline solid some scientists hesitate to call it
a law at all.

4. The Nernst heat theorem:
Before passing on to the 3rd law of thermodynamics, we may consider briefly the Nernst heat
theorem.
From the Gibb’s-Helmholtz equation,
∆G-∆H=T(∂(∆G)/∂T)p …….(1)
Where ∆G is the change in free energy
∆H is the change in enthalpy
It is seen that at the absolute zero(i.e,T=0)
Richards , by measuring EMFs of cells at different
temperatures , found that the value of ∂(∆G)/∂T
decreases with decrease in temperature and
Therefore concluded that ∆G and ∆H tend to
approach each other more and more closely as the
temperature is lowered. The value of ∂(∆G)/∂T
approaches zero gradually as the temperature is
towered towards the absolute zero . This is known as
the “Nernst heat theorem”.

6. Third law of thermodynamics:
According to equation(6), ∆𝐶 𝑃tends to approach zero at 0K.This means that at absolute zero, the
heat capacities of products and reactants in solid state are identical. This leads to the suggestion
that at absolute zero, all substances have the some heat capacity. The quantum theory, as applied
to heat capacities of solids tends to become zero at 0K.
The Nernst heat theorem , can be written as
lim
𝑇→0
𝐶𝑃 =0 …………(7)
According to equation(5), ∆𝑆 becomes zero at absolute zero. The entropy change of a process
involving solids becomes zero at 0K. In other words, the absolute entropies of products and
reactants in the solid state are identical. Planck therefore suggested that entropies of all pure solids
approach zero at 0K.
lim
𝑇→0
𝑆 =0 ….………..(8)
This led to the formulation of the third law of thermodynamics: “At the absolute zero of
temperatures the entropy of every substance may becomes zero on it does becomes zero in the
case of a perfectly crystalline solid.”

7. Determination of absolute entropies of solids , liquids and gases:
we have 𝑑𝑠 =
𝑑𝑞
𝑇
………….(1)
If the change takes place at constant pressure, then
𝜕𝑆 𝑃 =
𝜕𝑞 𝑃
𝑇
𝜕𝑆
𝜕𝑇 𝑃 =
𝜕𝑞
𝜕𝑇 P.
1
𝑇
… … … … … . 2
By definition of 𝐶 𝑃 =
𝜕𝑞
𝜕𝑇 𝑃 … … … … … . . (3)
equation(2) becomes,
𝜕𝑦
𝜕𝑥 P = CP ×
1
𝑇
at constant pressure,𝑑𝑠 =
𝐶 𝑃
𝑇
𝑑𝑇
For a perfectly crystalline substance, the absolute entropy S=0 at T=0.
Therefore, we may write

9. Where a is an empirical constant , equation(7) is known as the Debye T3
law and according to equation(6).
𝑆 𝑇 =
0
𝑇∗
𝑎𝑇3
𝑑𝑇
𝑇
+
𝑇∗
𝑇
𝐶 𝑃
𝑑𝑇
𝑇
𝑆 𝑇 =
1
3
𝑎𝑇
∗ 3
+ 𝑇
∗
𝑇
𝐶 𝑃
𝑑𝑇
𝑇
………….(8)
The absolute entropy of a substance, whether solid , liquid and gas at temperature T, can be determined as
illustrated below.
For solids:
For determination the entropy, the heat capacity of solids should be known. The heat capacity of
the solids is determined from Debye T-cubed law which is given by
CP, S = aT3
………….(9)
where 𝐶 𝑃, 𝑆 is heat capacity of the solids
The entropy will be
𝑆 𝑇 =
0
𝑇 𝑚𝑖𝑛 𝐶 𝑃, 𝑆
𝑇
𝑑𝑇 +
𝑇 𝑚𝑖𝑛
𝑇
𝐶 𝑃, 𝑆
𝑇
𝑑𝑇

10. 𝑆 𝑇 =
0𝐾
𝑇 𝑚𝑖𝑛 𝐶 𝑃, 𝑆
𝑇
𝑑𝑇 +
𝑇 𝑚𝑖𝑛
𝑇
𝐶 𝑃, 𝑆
𝑑
𝑇
𝐾
𝑇
𝐾
𝑆 𝑇 =
0𝐾
𝑇 𝑚𝑖𝑛 𝐶 𝑃, 𝑆
𝑇
𝑑𝑇 + 2.303
𝑇 𝑚𝑖𝑛
𝑇
𝐶 𝑃, 𝑆 𝑑 log
𝑇
𝐾
where Tmin is the minimum temperature to which the value of heat capacity is available.
For Liquids:
The entropy for liquids at temperature T is determined as follows .
The solid is heated from temperature 0K to its melting point Tm .
 This solid is transformed to liquid at its melting point Tm .
Then the liquid is heated to temperature T. Thus, by addition these three processes we
get
 𝑆 𝑇 = 0𝐾
𝑇 𝑚 𝐶 𝑝
,
𝑚
(𝑠)
𝑇
𝑑𝑇 +
∆ 𝑓𝑢𝑠
𝐻 𝑚
𝑇 𝑚
+ 𝑇 𝑚
𝑇 𝐶 𝑝
,
𝑚
(𝑙)
𝑇
dT

11. For gases:
Similarly for gases, the entropy is given by:
𝑆 𝑇 =
0𝐾
𝑇 𝑚 𝐶 𝑝, 𝑚(𝑠)
𝑇
𝑑𝑇 +
∆ 𝑓𝑢𝑠 𝐻 𝑚
𝑇 𝑚
+
𝑇 𝑚
𝑇 𝑏 𝐶 𝑝, 𝑚(𝑙)
𝑇
𝑑𝑇 +
∆ 𝑣𝑎𝑝 𝐻
𝑇 𝑏
+
𝑇 𝑏
𝑇
𝐶 𝑝, 𝑚(𝑔)
𝑇
𝑑𝑇

12. Graphical representation of absolute entropies of solids,
liquids and gases:

13. Residual entropy:
According law, the entropies of solids should become equal to zero at 0K. But it is
observed that the entropies of substance such as CO,H2O,NO,NO2 etc. are not zero at 0K.
These finite entropies are called residual entropies. This existence of residual entropy in a
crystal at 0K is due to the alternative arrangements of molecules in the solid..
Importance of third law of thermodynamics is given below:
 It helps in calculating the thermodynamic properties.
It explains the to third behavior of solids at very low temperature.
It helps in analyzing chemical and phase equilibrium.
Conclusion:
If the entropy of every element in its most stable state at T=0 is taken as zero, then every
substance has a positive entropy which at T=0 may become zero for all perfect crystalline
substances.

14. References:
1. Principles of physical chemistry, Fourth edition by Samuel H,Moran carl F.Prutton
2. Principles of physical chemistry by B.R.Puri , R.Sharma , Madan.S,Pathania.
3. https://www.academia.edu
4. https://epgp.inflibnet.ac.in

15. Thank you