Q 11-11-141JEE MainJEE Main 2020 (2 Sep, Shift 1)Medium
An engine takes in $5$ moles of air at $20\ ^\circ\text{C}$ and $1\ \text{atm}$, and compresses it adiabatically to $1/10^{\text{th}}$ 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 $X\ \text{kJ}$. The value of $X$ to the nearest integer is ______.
Numerical value type. Enter your answer.
Answer: 46
For rigid diatomic air $\gamma = 7/5$ and $C_V = \tfrac52 R$.
Adiabatic: $T_2 = T_1\left(\dfrac{V_1}{V_2}\right)^{\gamma-1} = 293\times10^{0.4} \approx 736$ K.
$$\Delta U = nC_V\Delta T = 5\times\frac52\times8.314\times(736-293) \approx 4.6\times10^{4}\ \text{J} \approx 46\ \text{kJ}$$
Solution by Sreeraj P, M.Sc Physics