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Question

# Identify the correct statement(s).

A
For a gas in a rigid container, mean free path is independent of pressure and temperature
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B
Translational kinetic energy of a given amount of an ideal gas is independent of pressure
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C
All the molecules of a gas at a given temperature have the same kinetic energy
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D
The average kinetic energy of 1 mol of gas molecules at a given temperature is proportional to M. (where 'M' is molar mass of gas)
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Solution

## The correct options are A For a gas in a rigid container, mean free path is independent of pressure and temperature B Translational kinetic energy of a given amount of an ideal gas is independent of pressure(a) Mean free path =1√2πσ2(NV) where πσ2= areas of cross of section NV= Number of molecules per unit volume so mean free path is independent of "P" and "T" as N and V are fixed for rigid container. ∴ (a) is correct. (b) KE (translational)=(32nRT) translational K.E. depends only only temperature. (c) As the kinetic energy depends upon the velocity of molecules, KE=12mv2 and from Maxwell's distribution curve, it can be seen that molecules of all gases have a wide range of speeds so they have different kinetic energies. (d) KE (average per mole)=(32RT) It depends only on temperature.

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