$dQ = dU + dW$; At constant Volume, Work done by the gas is zero so
dQ = dU;
$nCvdT = f/2 nRdT $;
$Cv = f/2R$;
$dQ/dT = f/2 R $;
$nCpdT = f/2 nRdT + PdV$;(At constant Pressure)
$PdV +VdP = nRdT$;(Differentiating $PV = nRT$)
$nCpdT = f/2nRdT +PdV$(At constant Pressure)
$nCpdT = f/2nRdT + nRdT$
$Cp = f/2 R + R$
$Cp = Cv + R$
Piyush Lath
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