Question

An insulated box containing a diatomic gas of molecular mass $M$ is moving with velocity $v$. If the box is suddenly stopped, the resulting change in temperature is ($R$ is the gas constant)

• A. $\frac{M{v}^2}{2R}$
• B. $\frac{M{v}^2}{3R}$
• C. $\frac{M{v}^2}{5R}$
• D. $\frac{2M{v}^2}{5R}$

Answer 1

The correct option is C $\frac{M{v}^2}{5R}$


Energy associated with forward moment will be used to raise temperature of gas.
Which is change in internal energy
$\Delta U=n{C}_v\Delta T$
$n{N}_A\left(\frac{1}{2}m{v}^2\right)=n\frac{5}{2}R\Delta T$

$\Delta T=\frac{1}{2}\frac{\left(N_{A}m\right)v^2}{\frac{5}{2}R}=\frac{M{v}^2}{5R}$