Difference between specific heat capacities

DIFFERENCE BETWEEN SPECIFIC HEAT CAPACITIES

The first Tds equation is given by

Similarly, the second Tds equation is given by

Equating these two Tds equations,

Comparing the coefficients of dv and dp in equation (5.79) and (5.80), it can be written as

These two equations have common term of (Cp - Cv), the expression can be written as

The equation (5.81) is the first form of (Cp - Cv) equation.

The same (Cp - Cv) equation can be obtained in other form also shown below.

We know that there are two specific heats of gas, i.e. Cp and Cv can experimentally be measured.

From the definition of specific heats,

Let, the entropy (s) is a function of temperature (T) and specific volume (v).

From the equation (5.88), the difference between the two specific heats Cp and Cv is determined in terms of measurable properties p, v and T.