The rectangle box shown in fig has a partition which can slide without friction along the length of the box. Initially each of the two chambers of the box has one mole of monatomic ideal gas ( $\gamma$ =5/3) at a pressure P₀ , volume V₀ and temperature T₀ . The chamber on the left is slowly heated by an electric heater. The walls of the box and the partition are thermally insulated. The gas in the left chamber expands, pushing the partition until the final pressure in both chambers becomes (243/32) P₀. The final temperature of the gas in left chamber is:

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63 T₀

13 T₀

9 T₀

21 T₀

answer is C.

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Detailed Solution

$\large \begin{array}{*{20}{c}} {{P_0}{V_0}^{5/3} = \left( {\frac{{243}}{{82}}} \right){P_0}{V_R}^{5/3} \Rightarrow {V_R} = \frac{{8{V_0}}}{{27}}} \\ {\therefore \,{V_L} = 2{V_0} - \frac{{8{V_0}}}{{27}} = \frac{{46{V_0}}}{{27}}} \end{array}\$
From ideal gas equation $\Rightarrow {T_L} = 13{T_0}\$