Question

When temperature of an ideal gas is increased from ${27}^{o}C$ to ${277}^{o}C,$ its rms speed is changed from 400 m/s to $v_s.$ The $v_s$ is :

• A. 516 m/s
• B. 450 m/s
• C. 310 m/s
• D. 746 m/s

Answer 1

Answer: (A)

516 m/s

The root mean square velocity of the gas is given by

$v_{rms}=\sqrt{\frac{3RT}{M}}$

Where, R is gas constant, T is absolute temperature and m is the molecular weight of the gas.

$T_1={27}^{o}C=273+27=300K$

$T_2={227}^{o}C=273+227=500K$

$\frac{v_1}{v_2}=\sqrt{\frac{300}{500}}=\sqrt{\frac{3}{5}}$

Given $v_1=400m/s,v_2=v_s$

$v_s=\sqrt{\frac{5}{3}}\times 400$

$=1.29\times 400=516.39m/s=516m/s$

Note : If the absolute temperature of the gas become zero then the motion of molecules will cease.