Question

How many times the temperature of a gas would increase, when the $RMS$ velocity of the gas molecules in a closed vessel of fixed volume is increased from 5 x 10${}^4$ $cms$${}^{-1}$ to 10 x 10${}^4$ $cms$${}^{-1}$?

• A. 4 times
• B. 16 times
• C. 2 times
• D. 8 times

Answer 1

The correct option is A 4 times

We know, $\frac{C_1}{C_2}=\sqrt{\frac{T_1}{T_2}}$

By putting the values, $\frac{5\times {10}^4}{10\times {10}^4}=\sqrt{\frac{T_1}{T_2}}=\frac{1}{2}$

$T_2=4\times T_1$

So, the correct option is $C$