Question

One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure.

The change in internal energy of the gas during the transition is

• A. 20 J
• B. -12 kJ
• C. 20 kJ
• D. -20 kJ

Answer 1

Answer: (D)

We know, $\Delta U=n{C}_v\Delta T$
$=n\left(\frac{5R}{2}\right)\left(T_B-T_A\right)$ [for diatomic gas, $C_v=\frac{5R}{2}$ ]
$=\frac{5nR}{2}\left(\frac{P_B{V}_B}{nR}-\frac{P_A{V}_A}{nR}\right)[\because PV=nRT]$

$=\frac{5}{2}\left(P_B{V}_B-P_A{V}_A\right)=\frac{5}{2}\left(2\times 10^3\times 6-5\times 10^3\times 4\right)$
$=\frac{5}{2}\left(-8\times 10^3\right)=-20kJ$