Q114 / 180 · NEET 2015 (Phase 1) · Physics

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
$20 kJ$
Correct answer
B
$- 20 kJ$
C
$20 J$
D
$- 12 kJ$

Solution

Δ U = n C_{v} Δ T

T = \frac{P V}{n R}

Δ T = \frac{P_{2} V_{2} - P_{1} V_{2}}{n R}

Δ U = \frac{n R}{γ - 1} (\frac{P_{2} V_{2} - P_{1} V_{1}}{n R})

= \frac{P_{2} V_{2} - P_{1} V_{1}}{γ - 1}

= - \frac{8 \times 10^{3}}{\frac{2}{5}} = - 20 k J

Hence, the correct answer is option: 'B'.

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