Question

A box of negligible mass containing $2$ moles of an ideal gas of molar mass $M$ and adiabatic exponent $\gamma$ moves with constant speed $v$ on a smooth horizontal surface. If the box suddenly stops, then change in temperature of gas will be

• A. $\frac{(\gamma-1) M v^{2}}{4 R}$
• B. $\frac{\gamma M v^{2}}{2 R}$
• C. $\frac{M v^{2}}{2(\gamma-1) R}$
• D. $\frac{(\gamma-1) M v^{2}}{2 R}$

Answer 1

Answer: (D)

Mass of gas in the box $=2 M$
Initial kinetic energy $=\frac{1}{2} \times 2 M \times v^{2}=M v^{2}$
$M v^{2}=\frac{1}{2} n f R \Delta T$
$\therefore \Delta T=\frac{2 M v^{2}}{n f R}$
Substitution $f=\frac{2}{1-r}$ and $n=2$
$\Delta T=\frac{(\gamma-1) M v^{2}}{2 R}$