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

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$227.36 \ K$

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(A) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma - 1} = 	ext{constant}$.Therefore,we can write: $T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}$.Rearranging for the final temperature $T_2$: $T_2 = T_1 \left( \frac{V_1}{V_2} ight)^{\gamma - 1}$.Given: $T_1 = 300 \ K$,$V_2 = 2 V_1$,and $\gamma = 1.40$.Substituting the values: $T_2 = 300 \left( \frac{V_1}{2 V_1} ight)^{1.40 - 1}$.$T_2 = 300 \left( \frac{1}{2} ight)^{0.4}$.$T_2 = 300 	imes (0.5)^{0.4} \approx 300 	imes 0.7578 = 227.36 \ K$.

An ideal gas is expanded adiabatically at an initial temperature of $300 \ K$ so that its volume is doubled. The final temperature of the hydrogen gas is $(\gamma = 1.40)$.

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