Question

The r.m.s. speed of hydrogen at S.T.P. is '\(u\)' \(\text{m/s}\). If the gas is heated at constant pressure till its volume becomes three times, the final temperature of the gas and the r.m.s. speed are respectively

• A. \(1092 \text{K}\) , \(3u \text{m/s}\)
• B. \(1092 \text{K}\) , \(\frac{u}{3} \text{m/s}\)
• C. \(819 \text{K}\) , \(\sqrt{3}\,u \text{m/s}\)
• D. \(819 \text{K}\) , \(\frac{u}{\sqrt{3}} \text{m/s}\)

Hint:

At constant pressure V is proportional to T, and r.m.s. speed is proportional to the square root of T.

Answer 1

The Correct Option is C

Step 1: Temperature:
$\frac{V_2}{V_1} = \frac{T_2}{T_1} = 3$, so $T_2 = 819$ K.

Step 2: Speed:
$v_{rms}^2 \propto T$, so tripling $T$ multiplies the speed by $\sqrt3$.

Final Answer:
The answer is $819$ K and $\sqrt{3}\,u$ m/s, option (C). \[ \boxed{819\ \text{K},\ \sqrt{3}\,u} \]