The Clausius and Kirchhoff equations

In the last section we derived the relations between the thermal coefficients Cy, i v Ih one hand and on the 

The internal energy U being a function of T, V, we have the identities 

These equations are called the Clausius equations although the second, which relates the heat capacity change to the temperature coefficient of the heat of reaction, is also called Kirchhoff s equation and the last equation, giving the effect of volume on the heat of reaction, was first derived by De Donder. 

We may proceed in an analogous manner in the variables T, p, and so obtain from (2.17) a second group of Clausius equations  

The second of these equations is sometimes known as Kirchhoffs second equation. 

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