An ideal gas is found to obey p V^{3/2} = tex | vedclass

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(A) For an adiabatic process, the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma-1} = 	ext{constant}$.Given that the pr

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$\sqrt{2} T$

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(A) For an adiabatic process, the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma-1} = 	ext{constant}$.Given that the process follows $p V^{3/2} = 	ext{constant}$, we identify the adiabatic index $\gamma = 3/2$.Let the initial temperature be $T_i = T$ and the initial volume be $V_i = V$.The gas is compressed to half its initial volume, so $V_f = V/2$.Using the relation $T_i V_i^{\gamma-1} = T_f V_f^{\gamma-1}$, we get:$T_f = T_i \left( \frac{V_i}{V_f} ight)^{\gamma-1}$Substituting the values: $T_f = T \left( \frac{V}{V/2} ight)^{3/2 - 1}$$T_f = T (2)^{1/2} = \sqrt{2} T$.

An ideal gas is found to obey $p V^{3/2} = \text{constant}$ during an adiabatic process. If such a gas initially at a temperature $T$ is adiabatically compressed to half of its initial volume, then its final temperature is

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