Question

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q:\Delta U:\Delta W$ is

• A. 5 : 3 : 2
• B. 7 : 5 : 2
• C. 2 : 3 : 5
• D. 2 : 5 : 7

Answer 1

Answer: (B)

For a diatomic gas,
$C_V=\frac{5}{2}R;C_P=\frac{7}{2}R$
$\Delta Q=n{C}_P\Delta T=n\left(\frac{7}{2}R\right)\Delta T$
$\Delta U=n{C}_V\Delta T=n\left(\frac{5}{2}R\right)\Delta T$
According to first law of thermodynamics,
$\Delta W=\Delta Q-\Delta U=nR\Delta T$
$\therefore \Delta Q:\Delta U:\Delta W=\frac{7}{2}:\frac{5}{2}:1$ or $7:5:2.$