The work of $146\ kJ$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^o C$. The gas is $(R=8.3\ J\ mol^{-1} K^{-1})$
AIEEE 2006, Medium
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$W = \frac{{nR\Delta T}}{{1 - \gamma }} \Rightarrow - 146000 = \frac{{1000 \times 8.3 \times 7}}{{1 - \gamma }}$
$or\,1 - \gamma = - \frac{{58.1}}{{146}} \Rightarrow \gamma = 1 + \frac{{58.1}}{{146}} = 1.4$
Hence the gas is diatomic.
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