Start with Equation below for the change in specific entropy

for an ideal gases with constant specific heats,

s$2$ s$1=$ Cp ln

T$2$

T$1$

$$ R ln

p$2$

p$1$

Use the ideal gas law p $=\backslash$rho RT and the definition of specific volume v $=1/\backslash$rho to

derive the related equation below,

s$2$ s$1=$ Cv ln

T$2$

T$1$

$+$ R ln

v$2$

v$1$