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,
$\Delta W = \Delta Q - \Delta U = n R \Delta T$
$\therefore \:\:\: \Delta Q : \Delta U : \Delta W = \frac{7}{2} : \frac{5}{2} : 1 $ or $7 : 5 : 2.$