Question:
A diatomic gas, having $C_{p}=\frac{7}{2} R$ and
$C_{v}=\frac{5}{2} R$, is heated at constant pressure. The
ratio $\mathrm{dU}: \mathrm{dQ}: \mathrm{dW}:$
Correct Option: , 2
Solution:
$\mathrm{dU}=\mathrm{nC}_{\mathrm{v}} \mathrm{dT}$
$\mathrm{dQ}=\mathrm{nC}_{\mathrm{p}} \mathrm{dT}$
$\mathrm{dW}=\mathrm{PdV}=\mathrm{nRdT}$ (isobaric process)
$\mathrm{dU}: \mathrm{dQ}: \mathrm{dW}: \mathrm{C}_{\mathrm{v}}: \mathrm{C}_{\mathrm{p}}: \mathrm{R}$
$=\frac{5 R}{2}: \frac{7 R}{2}: R=5: 7: 2$