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An Introduction to Thermal Physics
Found in: Page 159
An Introduction to Thermal Physics

An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

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Short Answer

The formula for CP-CV derived in the previous problem can also be derived starting with the definitions of these quantities in terms of U and H. Do so. Most of the derivation is very similar, but at one point you need to use the relation P=-(F/V)T.


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Step by Step Solution




The specific heat of a substance can be of two types:(i) specific heat at constant pressure CP(ii) specific heat at constant volume CV

They are given by


Where, U = internal energy, H = enthalpy, V = volume and P = pressure.

Lets consider U=U(V, T), and differentiate above expression with respect to T, we get

Similarly write expression for enthalpy H=U+P V.

Write the expression for d H at constant pressure d H=d U+P d V

Substitute dU=UVTdV+UTVdT

We get,


Simplify, divide both sides of the above expression by d T,


Substitute CP for HTP and CV for UTV


Substitute -FVTfor P in equation (2)


Now substitute TS for (U-F)


So, the value of CP-CV=TSVTVTP

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