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(B) Let the initial pressure of samples $X, Y$,and $Z$ be $P_X, P_Y$,and $P_Z$ respectively. Let the initial volume be $V$. The final volume for all i

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$2: 2\sqrt{2}: 1$

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(B) Let the initial pressure of samples $X, Y$,and $Z$ be $P_X, P_Y$,and $P_Z$ respectively. Let the initial volume be $V$. The final volume for all is $2V$.For sample $X$ (isothermal process): $P_X V = P_{X,f} (2V) \implies P_{X,f} = P_X / 2$.For sample $Y$ (adiabatic process): $P_Y V^{\gamma} = P_{Y,f} (2V)^{\gamma} \implies P_{Y,f} = P_Y / 2^{\gamma}$. Given $\gamma = 3/2$,$P_{Y,f} = P_Y / 2^{3/2} = P_Y / (2\sqrt{2})$.For sample $Z$ (isobaric process): $P_Z = P_{Z,f}$.Given $P_{X,f} = P_{Y,f} = P_{Z,f} = P_0$,we have:$P_X / 2 = P_0 \implies P_X = 2P_0$.$P_Y / (2\sqrt{2}) = P_0 \implies P_Y = 2\sqrt{2} P_0$.$P_Z = P_0$.Thus,the ratio $P_X : P_Y : P_Z = 2P_0 : 2\sqrt{2} P_0 : P_0 = 2 : 2\sqrt{2} : 1$.

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