Question
From the following statements concerning ideal gas at any given temperature $$T,$$ select the correct one(s)
A.
The co-efficient of volume expansion at constant pressure is the same for all ideal gases
B.
The average translational kinetic energy per molecule of oxygen gas is $$3kT, k$$ being Boltzmann constant
C.
The mean - free path of molecules increases with increases in the pressure
D.
In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different
Answer :
The co-efficient of volume expansion at constant pressure is the same for all ideal gases
Solution :
For an ideal gas $$PV = nRT$$
⇒ Co - efficient of volume expansion
$${\left( {\frac{{\Delta V}}{{\Delta T}}} \right)_P} = \frac{{nR}}{P} = {\text{Constant}}$$
Note : Average translation K.E. for $${O_2}$$ is $$\frac{3}{2}kT$$
(Three degrees of freedom for translational motion).
Now decrease in pressure increases the volume.
⇒ It increases mean free path of the molecules. Also
average K.E. does not depend on the gas, so molecules
of each component of mixture of gases have same
average translational energy.