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, $\Delta U=n C_{v} \Delta T$
$=n\left(\frac{5 R}{2}\right)\left(T_{B}-T_{A}\right)$ [for diatomic gas, $C_{v}=\frac{5 R}{2}$ ]
$=\frac{5 n R}{2}\left(\frac{P_{B} V_{B}}{n R}-\frac{P_{A} V_{A}}{n R}\right)[\because P V=n R T]$

$=\frac{5}{2}\left(P_{B} V_{B}-P_{A} V_{A}\right)=\frac{5}{2}\left(2 \times 10^{3} \times 6-5 \times 10^{3} \times 4\right)$
$=\frac{5}{2}\left(-8 \times 10^{3}\right)=-20\, k J$