Question

Molecular velocities of two gases at the same temperature $(T)$ are $u_{1}$ and $u_{2}$. Their masses are $m_{1}$ and $m_{2}$ respectively. Which of the following expressions is correct at temperature T?

• A. $\frac{m_{1}}{u_{1}^{2}}=\frac{m_{2}}{u_{2}^{2}}$
• B. $m_{1} u_{1}=m_{2} u_{2}$
• C. $\frac{m_{1}}{u_{1}}=\frac{m_{2}}{u_{2}}$
• D. $m_{1} u_{1}{ }^{2}=m_{2} u_{2}{ }^{2}$

Answer 1

Answer: (D)

We know $u \times \sqrt{\frac{T}{m}}$
but as $T$ is same for both gases
Hence $u \propto \frac{1}{\sqrt{m}}$
$\therefore \frac{u_{1}}{u_{2}}=\sqrt{\frac{m_{2}}{m_{1}}}$
or $\frac{u_{1}{ }^{2}}{u_{2}{ }^{2}}=\frac{m_{2}}{m_{1}}$
or $m_{1} u_{1}{ }^{2}=m_{2} u_{2}{ }^{2}$