An ideal gas initially at 0^{circ} C temperat | vedclass

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(C) The process is sudden compression, which is an adiabatic process. For an adiabatic process, the relation between temperature $T$ and volume $V$ is

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$273$

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(C) The process is sudden compression, which is an adiabatic process. For an adiabatic process, the relation between temperature $T$ and volume $V$ is $TV^{\gamma-1} = 	ext{constant}$.Given: Initial temperature $T_1 = 0^{\circ} C = 273 \ K$, initial volume $V_1 = V_0$, final volume $V_2 = V_0/4$, and adiabatic index $\gamma = 3/2$.Using the adiabatic relation: $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.$273 	imes V_0^{(3/2 - 1)} = T_2 	imes (V_0/4)^{(3/2 - 1)}$.$273 	imes V_0^{0.5} = T_2 	imes (V_0/4)^{0.5}$.$273 = T_2 	imes (1/4)^{0.5} = T_2 	imes (1/2)$.$T_2 = 273 	imes 2 = 546 \ K$.The change in temperature is $\Delta T = T_2 - T_1 = 546 \ K - 273 \ K = 273 \ K$.

An ideal gas initially at $0^{\circ} C$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamics process is . . . . . . $K.$

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