Two containers A and B contain equal volumes | vedclass

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(A) Initial state: $V_A = V_B = V$,$p_A = p_B = p$.For container $A$ (isothermal process): $p_A V_A = p_A^{\prime} V_A^{\prime}$.Given $V_A^{\prime} =

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$(2)^{\gamma-1}$

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(A) Initial state: $V_A = V_B = V$,$p_A = p_B = p$.For container $A$ (isothermal process): $p_A V_A = p_A^{\prime} V_A^{\prime}$.Given $V_A^{\prime} = V/2$,so $p V = p_A^{\prime} (V/2) \Rightarrow p_A^{\prime} = 2p$.For container $B$ (adiabatic process): $p_B V_B^{\gamma} = p_B^{\prime} (V_B^{\prime})^{\gamma}$.Given $V_B^{\prime} = V/2$,so $p V^{\gamma} = p_B^{\prime} (V/2)^{\gamma} \Rightarrow p_B^{\prime} = p \cdot 2^{\gamma}$.The ratio of final pressures is $\frac{p_B^{\prime}}{p_A^{\prime}} = \frac{p \cdot 2^{\gamma}}{2p} = 2^{\gamma-1}$.

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