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An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to 1/10th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be XkJ. The value of X to the nearest integer is : 

Numerical Value Type

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Thermodynamics, engines and cycles

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Sol. $T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}$

$T_2=T_1\left({V_1\over V_2}\right)^{\gamma-1}$

$=T_1(10)^{{7\over5}-1}$

$T_2=T_1(10)^{2/5}$

$\Delta V={5\over2}nR={5\over2}\times5\times3[10^{2/5}-1](293)$

${625\over6}\times1.5\times293=461440$

$\approx46ks$

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