Question

The temperature of an ideal gas is increased for 100k to 400k. If at 100k the root mean square velocity of the gas molecules is v, at 400k it becomes

• A. 4v
• B. 2Vb
• C. v/2
• D. v/4

Answer 1

Answer: (B)

2Vb

Answer 2

C_rms = $\sqrt{\frac{3RT}{M}}$ or C_rms α$\sqrt{T}$

$\frac{\left( C_{rms} \right)_{T_{2}}}{\left( C_{rms} \right)_{T_{1}}} = \sqrt{\frac{T_{2}}{T_{1}}}$ = $\sqrt{\frac{400}{100}}$ = 2

(C_rms)$T_{2}$ = 2(C_rms)$T_{1}$ = 2 × v = 2v