Figure shows a long fixed container which has two freely movable (without friction) pistons. The container and pistons are made up of a thermally conducting material, that allows very slow transfer of heat. First compartment of container is filled with 2 moles of an ideal monoatomic gas at 200K and the 2^nd compartment is filled with 1 moles of ideal diatomic gas at 500K. Initially pressure of gases in both the compartment is same and equal to atmospheric pressure. Temperature of atmosphere is 300K. Finally gases achieve equilibrium. ‘R’ is the gas constant

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Heat transferred by gas in compartment -2 to the atmosphere is 700R

Heat transferred by gas in compartment -2 to the atmosphere is 500R

Work done by gas in compartment -2 on the gas in compartment -1 is 200R

Net heat transferred to gas in compartment -1 is 500R

answer is B.

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Detailed Solution

$\begin{array}{l} P_{0} V_{1} = 2 R (200) - (I) \\ P_{0} V_{1}^{1} = 2 R (300) - (I I) \\ P_{0} V_{2} = 1 R (500) - (I I I) \\ P_{0} V_{2}^{1} = 1 R (300) - (I V) \end{array}$

During process pressure of two gas compartment remains same equals to atmospheric
$V_{1} + V_{2} = V_{1}^{1} + V_{2}^{1}$ ; work done by two gas system on surrounding is zero. Net heat transferred by the gas in compartment $2 t o t h e a t m o s s p h e r e = W + Δ U = 1 (\frac{5 R}{2}) (500 - 300) J = 500 R J$