Using the first principle of thermodynamics, prove the following relations:for m $=1$Kg$1-2-3-$Co$=($aT$)$ vCp $=($at$)$ PCp $=$ Go $+$ Rfor m $=1$KgMAYER's relationQuestion $4$

Using the first principle of thermodynamics, prove the following relations:

$1-$

$C_v=(\frac{dU}{dT}{)}_v$

for $m=1Kg$

$2-$

$C_p=(\frac{dH}{dT}{)}_p$

for $m=1Kg$

$3-$

$C_p=Cv+R$

MAYER's relation