The root mean square velocity of molecules of a gas is $200 \mathrm{~m} / \mathrm{s}$. What will be the root…
The root mean square velocity of molecules of a gas is $200 \mathrm{~m} / \mathrm{s}$. What will be the
root mean square velocity of the molecules, if the molecular weight is doubled and
the absolute temperature is halved?
$50 \mathrm{~m} / \mathrm{s}$
$100 \mathrm{~m} / \mathrm{s}$
$200 \mathrm{~m} / \mathrm{s}$
$\frac{100}{\sqrt{2}} \mathrm{~m} / \mathrm{s}$
Solution
R.M.S. velocity $C=\sqrt{\frac{3 R T}{M}}$
$\therefore \quad C \quad \propto \sqrt{\frac{T}{M}}$
$\frac{C^{\prime}}{C}=\sqrt{\frac{T^{\prime}}{T} \frac{M}{M^{\prime}}}=\sqrt{\frac{1}{2} \times \frac{1}{2}}=\frac{1}{\sqrt{4}}=\frac{1}{2}$
$\therefore C^{\prime}=\frac{C}{2}=\frac{200}{2}=100 \mathrm{~m} / \mathrm{s}$