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  4. One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure, <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-yuwjldrmr3pul5bu.jpg /> The change in internal energy of the gas during the transition is:

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Q. One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure,
Question
The change in internal energy of the gas during the transition is:

NTA AbhyasNTA Abhyas 2022

Solution:

$\Delta U=nC_{v}\Delta T$
$T=\frac{P V}{n R}$
$\Delta T=\frac{P_{2} V_{2} - P_{1} V_{2}}{n R}$
$\Delta U=\frac{n R}{\gamma - 1} \, \left(\frac{P_{2} V_{2} - P_{1} V_{1}}{n R}\right)$
$=\frac{P_{2} V_{2} - P_{1} V_{1}}{\gamma - 1}$
$=-\frac{8 \times 10^{3}}{\frac{2}{5}}=-20 \, kJ$