The two conducting cylinder-piston systems shown below are linked. Cylinder 1 is filled with a certain molar quantity of a monatomic ideal gas, and cylinder 2 is filled with an equal molar quantity of a diatomic ideal gas. The entire apparatus is situated inside an oven whose temperature is $T_{a} = 27^{\circ} C .$ The cylinder volumes have the same initial value $V_{0} = 100 cc$ . When the oven temperature is slowly raised to $T_{b} = 127^{\circ} C .$ . The volume change $∆$ v in cc) of cylinder 1 is ____________

Moderate

Solution

$\begin{array}{l} P_{0} V_{0} = n R T_{a} \\ (P_{0} + Δ P) (V_{0} + Δ V) = n R T_{b} - - - (1) \\ (P_{0} + Δ P) (V_{0} - Δ V) = n R T_{b} - - - (2) \\ (1) \div (2) \\ \frac{(V_{0} + Δ V)}{(V_{0} - Δ V)} = 1 \\ Δ V = 0 \end{array}$
Pressure depends on number of moles and is independent of nature of gas.

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