The ratio of the specific heat capacities of | vedclass

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(D) Given, the ratio of specific heat capacities $\gamma = 1.5 = 3/2$.For an adiabatic process, $P_i V_i^\gamma = P_f V_f^\gamma$. Given $V_f = 2V_i$

Vedclass · Accepted Answer

$\sqrt{2}: 1$

Vedclass · Answer

(D) Given, the ratio of specific heat capacities $\gamma = 1.5 = 3/2$.For an adiabatic process, $P_i V_i^\gamma = P_f V_f^\gamma$. Given $V_f = 2V_i$ and $P_f = P_1$, we have $P_{i, 	ext{ad}} V_i^{1.5} = P_1 (2V_i)^{1.5}$.Thus, $P_{i, 	ext{ad}} = P_1 (2)^{1.5} = P_1 (2\sqrt{2})$.For an isothermal process, $P_i V_i = P_f V_f$. Given $V_f = 2V_i$ and $P_f = P_2$, we have $P_{i, 	ext{iso}} V_i = P_2 (2V_i)$.Thus, $P_{i, 	ext{iso}} = 2P_2$.Given $P_1 = P_2$, the ratio of initial pressures is $\frac{P_{i, 	ext{ad}}}{P_{i, 	ext{iso}}} = \frac{P_1 (2)^{1.5}}{2 P_1} = \frac{2\sqrt{2}}{2} = \sqrt{2} : 1$.

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