Third law of thermodynamics

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 3 rd 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), tends 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 =0 …………(7) According to equation(5), 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. =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 ………….(1) If the change takes place at constant pressure, then By definition of equation(2) becomes, at constant pressure, 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 T 3 law and according to equation(6). ………….(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 …………. (9) where is heat capacity of the solids The entropy will be  

10. where T min 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 T m . This solid is transformed to liquid at its melting point T m . Then the liquid is heated to temperature T. Thus, by addition these three processes we get  

11. For gases: Similarly for gases, the entropy is given by:  

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,H 2 O,NO,NO 2 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: Principles of physical chemistry, Fourth edition by Samuel H,Moran carl F.Prutton Principles of physical chemistry by B.R.Puri , R.Sharma , Madan.S,Pathania. https://www.academia.edu https://epgp.inflibnet.ac.in

15. Thank you