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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 $(γ = 1 .40)$

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-47^oC

227.36 K

500.30 K

454.76 K

answer is A.

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Detailed Solution

$\begin{array}{l} {TV}^{γ - 1} = constant \Rightarrow \frac{T_{2}}{T_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ} \Rightarrow T_{2} = T_{1} {(\frac{V_{1}}{V_{2}})}^{γ} \\ \Rightarrow T_{2} = 300 {(\frac{1}{2})}^{0 .4} = 227 .36 K \end{array}$

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