Question

https://photos.app.goo.gl/sF79QyKaeYehnVkj8

Answer 1

We know that ideal gas equation

$PV=nRT$

P=constant differentiate with respect T

$(\frac{dV}{dT})_p=\frac{R}{P}$

V constant differentiate with respect to T

$(\frac{dP}{dT})_V=\frac{R}{V}$

Now We know that

$c_p=[\frac{dQ}{dT}]_p$

$C_p-C_v=T[\frac{dp}{dT}]_v[\frac{dV}{dT}]_p$

Assume

$C_v=0$

$C_p=T[\frac{dp}{dT}]_v[\frac{dV}{dT}]_p$

We know that

$[\frac{dp}{dT}]_v=[\frac{dp}{dT}]_s$

$C_p=T[\frac{dp}{dT}]_s[\frac{dV}{dT}]_p$

Hance proved