Q 11-12-087JEE MainJEE Main 2022 (26 Jun, Shift 1)Medium
A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $1.4$. The vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings and vessel, the temperature of the gas increases by: ($R$ = universal gas constant)
Answer: (B) $\dfrac{Mv^2}{5R}$
For one mole, the ordered kinetic energy $\frac12Mv^2$ becomes internal energy:
$$\frac12Mv^2 = C_V\Delta T = \frac{R}{\gamma-1}\Delta T = \frac{R}{0.4}\Delta T$$
$$\Delta T = \frac{0.4\,Mv^2}{2R} = \frac{Mv^2}{5R}$$
Solution by Sreeraj P, M.Sc Physics