Calculate the final temperature of a monoatomic gas that is compressed reversible and adiabatically from 8 litre to 1 litre at 300k

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1200k

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answer is D.

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Detailed Solution

Adiabatic reversible: for mono atomic gas
$γ = \frac{5}{3} T \cdot V^{γ - 1} = constant$

$T_{1} \cdot V_{1}^{γ - 1} = T_{2} \cdot V_{2}^{γ - 1} (\frac{T_{2}}{T_{1}}) = {(\frac{V_{1}}{V_{2}})}^{γ - 1}$

$\begin{array}{l} T_{2} = 300 \times {(\frac{8}{1})}^{\frac{5}{3} - 1} = 300 \times (8)^{2 / 3} \\ = 1200 k \end{array}$

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