By how many folds the temperature of a gas would increase when the...

By how many folds the temperature of a gas would increase when the root mean square velocity of the gas molecules in a container of fixed volume is increased from

5 \times 10^4 \mathrm{~cm} / \mathrm{s}

10 \times 10^4 \mathrm{~cm} / \mathrm{s}

Options

ATwo
BThree
CSix
DFour

Correct answer

D. Four

Step-by-step solution

r.m.s. velocity

\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}

i.e.,

\frac{\mathrm{V}_1}{\mathrm{~V}_2}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}

\frac{5 \times 10^4}{10 \times 10^4}=\frac{1}{2}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}

\therefore \mathrm{T}_2=4 \mathrm{T}_1

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