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 ............$\;kJ$
AIPMT 2015, Diffcult
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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)$
$\left[ {PV = nRT} \right]$
$ = \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\,kJ$
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