Three samples of the same gas A, B and C (gam | vedclass

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(B) Let the initial volume be $V$ and the final pressure be $P$ for all three samples.For sample $A$ (adiabatic process): $P_A V^{\gamma} = P_f (2V)^{

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

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(B) Let the initial volume be $V$ and the final pressure be $P$ for all three samples.For sample $A$ (adiabatic process): $P_A V^{\gamma} = P_f (2V)^{\gamma}$. Given $P_f = P$ and $\gamma = 3/2$,we have $P_A V^{3/2} = P (2V)^{3/2} \implies P_A = P \cdot 2^{3/2} = 2\sqrt{2}P$.For sample $B$ (isobaric process): The pressure remains constant,so $P_B = P_f = P$.For sample $C$ (isothermal process): $P_C V = P_f (2V)$. Given $P_f = P$,we have $P_C V = P(2V) \implies P_C = 2P$.Therefore,the ratio of initial pressures is $P_A : P_B : P_C = 2\sqrt{2}P : P : 2P = 2\sqrt{2} : 1 : 2$.

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