Question

# From the following statements , regarding an ideal gas at any given temperature T, choose the correct alternative(s)

A
The coefficient of volume expansion at constant pressure is the same for all ideal gases
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B
The average translational kinetic energy per molecule of oxygen gas is 3kT, where k being Boltzmann constant
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C
The mean -free path of molecules increases with decrease in the pressure
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D
In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different.
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Solution

## The correct option is C The mean -free path of molecules increases with decrease in the pressure For one mole of an ideal gas PV=RT Differentiating the above equation with respect to T on both sides we get, (ΔVΔT)P=RP The coefficient of volume expansion at constant pressure is given by γ=1V(ΔVΔT)P=1T At a given temperature and pressure, coefficient of volume expansion is same for all the ideal gases. ∴ Option (a) is correct. The average translational kinetic enrgy per molecule is (32)kT and not 3kT. With decrease in pressure, collisions between molecules will be less frequent, hence mean free path will increase. λ=kT√2πd2P⇒λ∝1P ∴ Option (c) is also correct. The average translational kinetic energy of the molecules is independent of their nature and is only a function of temperature. ⇒ Each component of the gaseous mixture will have the same value of average translational kinetic energy, at the given temperature. Thus, Options (a) and (c) are the correct alternatives.

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