Question

An engine takes in $5$ moles of air at $20^{\circ }C$ and $1atm,$ and compresses it adiabatically to ${\left(\frac{1}{10}\right)}^{th}$ 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

Answer 1

Answer: 46

$T_2{V}_2^{r-1}=T_1{V}_1^{\gamma -1}$
$T_2=T_1{\left(\frac{V_1}{V_2}\right)}^{\gamma -1}$
$=293{\left(\frac{V}{V/10}\right)}^{\frac{7}{5}-1}$
$\Delta U=n{C}_v\Delta T=5\times \frac{5}{2}R\left(293\times {\left(10\right)}^{\frac{2}{5}}-293\right)$
$=\frac{25}{2}R\times 293\left({\left(10\right)}^{\frac{2}{5}}-1\right)=\frac{25R}{2}\times 293(2.5-1)$
$=45675J=46kJ$