Question

The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity of nitrogen. If T is the temperature of the gas

• A. $T(H_{2}) = T(N_{2})$
• B. $T(H_{2}) > T(N_{2})$
• C. $T(H_{2}) < T(N_{2})$
• D. $T(H_{2}) = \sqrt{7}T(N_{2})$

Answer 1

Answer: (C)

$T(H_{2}) < T(N_{2})$

Answer 2

$u = \sqrt{\frac{3RT}{M}}$; ∴ $\frac{u(H_{2})}{u(N_{2})} = \sqrt{\frac{T(H_{2})}{M(H_{2})} \times \frac{M(N_{2})}{T(N_{2})}}$ or

$\sqrt{7} = \sqrt{\frac{T(H_{2})}{T(N_{2})} \times \frac{28}{2}}$ or $7 = \frac{T(H_{2})}{T(N_{2})} \times 14$ or $\frac{T(H_{2})}{T(N_{2})} = \frac{1}{2}$

or $T(N_{2}) = 2 \times T(H_{2})$ i.e., $T(N_{2}) > T(H_{2})$