Derive the expression for isothermal change in Constant Volume Heat Capacity

Thread starter eagerbeaver92
Start date Sep 22, 2009
Tags

Capacity Change Constant Derive Expression Heat Heat capacity Isothermal Volume

AI Thread Summary

The discussion focuses on deriving the expression for the isothermal change in Constant Volume Heat Capacity, specifically (dCv/dV)T = T(d2P/dT2)V. The initial attempt involves using the ideal gas law, P=nRT/V, leading to the first derivative (dP/dT) = R/V. However, the contributor mistakenly concludes that the second derivative (d2P/dT2) equals zero, resulting in (dCv/dV) being zero. This indicates a misunderstanding of the derivatives involved in the context of heat capacity changes. Clarification and further assistance are sought to correctly derive the expression.

Sep 22, 2009

eagerbeaver92

Homework Statement

Derive the following expression for calculating the isothermal change in Constant Volume Heat Capacity:

(dC_v/dV)_T = T(d²P/dT²)_V

Homework Equations

The Attempt at a Solution

I have no idea, please help

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Sep 22, 2009

eagerbeaver92

How about this?

assuming ideal gas:

P=nrt/V

then

(dP/dT) = R/V , ignoring moles

and

(d₂P/d²T) = 0

so (dC^v/dV)=T*0=0

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