Question

A diatomic gas of moleculer weight $30\text{gm/ mole}$ is filled in a container at ${27}^{\circ }C$. It is moving at a velocity $100\text{m/s}$. If it is suddenly stopped, the rise in temperature of gas( in SI units) 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 $\frac{60}{R}$

From first law of thermodynamics
K.E. = $\Delta U$
$\frac{1}{2}m{v}^2=n{C}_{v}dT$
$\frac{1}{2}\times \frac{30}{1000}\times {100}^2=1\times \frac{R}{\gamma -1}\times \Delta T$
$\gamma =1.4$ for diatomic gas
$150=\frac{R}{1.4-1}\times \Delta T$
$\Delta T=\frac{60}{R}$