Question

The temperature of a gas is doubled (i) on absolute scale (ii) on centigrade scale. The increase in root mean square velocity of gas will be:

• A. more in case (i)
• B. more in case (ii)
• C. same in both cases
• D. information not sufficient

Answer 1

The correct option is A more in case (i)

The temperature of a gas is doubled (i) on absolute scale (ii) on centigrade scale. The increase in root mean square velocity of gas will be
more in case (i)
The expression for $RMS$ speed is
$u=\sqrt{\frac{3RT}{M}}$
Thus, $\frac{u^{\prime }}{u}=\sqrt{\frac{T^{\prime }}{T}}$
(i) Temperature is doubled from 100 $K$ to 200 $K$
$\frac{u^{\prime }}{u}=\sqrt{\frac{200}{100}}=1.414$
(ii) Temperature is doubled from 100 $C$ to 200 $C$
$\frac{u^{\prime }}{u}=\sqrt{\frac{473}{373}}=1.13$