Question

The temperature of the ideal gas is increased from 27${}^o$C to 927${}^o$C. The root mean square speed of its molecules becomes

• A. half
• B. twice
• C. four times
• D. one fourth

Answer 1

The correct option is B twice

Root mean square velocity, c $\infty \sqrt{T}$
$\therefore \frac{c_1}{c_2}=\sqrt{\frac{T_1}{T_2}}$
$\Rightarrow \frac{c_1}{c_2}=\sqrt{\frac{273+27}{273+927}}$
$\Rightarrow \frac{c_1}{c_2}=\frac{300}{120}=\frac{1}{4}$
$\therefore \frac{c_1}{c_2}=\frac{1}{2}\Rightarrow c_2=2c_1$