Two identical vessels are completely filled with two ideal gases A and B. If the ratio of mass of gas A to that of gas B is 1:2 and the ratio of rms speed of molecules of gas A to that of gas B is 2:1, the ratio of

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Correct answer: C. 1 : 2

The pressure exerted by an ideal gas is given by

P = \dfrac{1}{3} \rho v_{rms}^2 = \dfrac{1}{3} \dfrac{m}{V} v_{rms}^2

Since the vessels are identical, the volume

V

is the same for both gases.

Therefore,

P \propto m v_{rms}^2

The ratio of pressures is given by:

\dfrac{P_B}{P_A} = \dfrac{m_B}{m_A} \times \left( \dfrac{v_{rms, B}}{v_{rms, A}} \right)^2

Given

\dfrac{m_A}{m_B} = \dfrac{1}{2} \Rightarrow \dfrac{m_B}{m_A} = 2

And

\dfrac{v_{rms, A}}{v_{rms, B}} = \dfrac{2}{1} \Rightarrow \dfrac{v_{rms, B}}{v_{rms, A}} = \dfrac{1}{2}

Substituting the values:

\dfrac{P_B}{P_A} = 2 \times \left( \dfrac{1}{2} \right)^2 = 2 \times \dfrac{1}{4} = \dfrac{1}{2}

The ratio of pressure exerted by gas B to that by gas A is

1 : 2

.

Answer:

1 : 2

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