Question

To prove that

Short answer

The equation has been proved.

Step-by-step solution

Given data

The given values are

Concept of Partial Differentiation

The process of finding the partial derivative of a function is called partial differentiation. In this process, the partial derivative of a function with respect to one variable is found by keeping the other variable constant.

The formula to find the Partial derivative is given by:

Calculation to find the value of  CP - Cv

As it's known that and dQ = dU + PdV and PV = nRT .

The specific heat is given as

So, the value of P can be written as:

Similarly, for the value of V as follows:

Put the values in the gas equation PV=nRT

Substitute the value of PV in the gas equation as follows:

This is the specific heat in thermodynamics.