An engine takes in 5 moles of air at 20 ° C and 1atm , and...

An engine takes in

5

moles of air at

20 ° C

and

1atm

, and compresses it adiabatically to

1 / {10}^{th}

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:

Correct answer

Step-by-step solution

${T}_{1}{V}_{1}^{\gamma - 1} = {T}_{2}{V}_{2}^{\gamma - 1}$

${T}_{2} = {T}_{1}{\left(\dfrac{{V}_{1}}{{V}_{2}}\right)}^{\gamma - 1}$

$= {T}_{1} ( 10{)}^{\dfrac{7}{5} - 1}$

${T}_{2} = {T}_{1} ( 10{)}^{2 / 5}$

$\DeltaV = \dfrac{5}{2}nR; \dfrac{5}{2} \times 5 \times 3\left[{10}^{2 / 5} - 1\right] ( 293 )$

$\dfrac{625}{6} \times 1 . 5 \times 293 = 461440$

$\approx 46ks$

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