An adiabatic cylinder fitted with an adiabatic piston at the right end of cylinder, is divided into — Thermodynamics and Thermochemistry Chemistry Question
Question
An adiabatic cylinder fitted with an adiabatic piston at the right end of cylinder, is divided into two equal halves with a monoatomic gas on left side and diatomic gas on right side, using an impermeable movable adiabatic wall. If the piston is pushed slowly to compress the diatomic gas to $\frac{3}{4}$th of its original volume. The ratio of new volume of monoatomic gas to its initial volume would be
Answer: C
💡 Solution & Explanation
Reversible adiabatic process maintains pressure equality $P_L = P_R = P_{new}$. We have $P_0 V_0^{5/3} = P_{new} V_L^{5/3}$ and $P_0 V_0^{7/5} = P_{new} V_R^{7/5}$. Equating yields $(V_L / V_0)^{5/3} = (V_R / V_0)^{7/5}$. Since $V_R / V_0 = 3/4$, $V_L / V_0 = (3/4)^{\frac{7}{5} \times \frac{3}{5}} = (3/4)^{21/25}$.
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