Question

One mole of diatomic gas molecular weight 30 gm/mole is filled in a container at 27${}^{\circ }$C. It is moving at a velocity 100 m/s. If it is suddenly stopped, the rise in temperature of gas is

• A. $\frac{60}{R}$
• B. $\frac{600}{R}$
• C. $\frac{6\times {10}^4}{R}$
• D. $\frac{6\times {10}^5}{R}$

Answer 1

The correct option is A $\frac{60}{R}$

$KE=\Delta U$

$\frac{1}{2}m{v}^2=n{C}_v\Delta T$

$\frac{1}{2}\times \frac{30}{1000}\times {100}^2=1\times \frac{R}{\gamma -1}\times \Delta T$

Here $\gamma$ is 1.4 for a diatomic gas, so

$150=\frac{R}{1.4-1}\times \Delta T$

$\Delta T=\frac{60}{R}$