Explanation:
Let us assume that the gas is ideal gas in the given problem.
(a) Hence, expression for internal energy of a monoatomic gas is as follows.
U =
As there are three kinds of translations possible for a mono atomic ideal gas. Therefore, no rotation is possible.
And, according to equipartition theorem, each possible rotation, translation or vibration can contribute to the internal energy of the system.
And, for Helium a mono atomic ideal gas,
For carbon dioxide, which is considered a linear triatomic molecule, there are 3 translations possible, 2 rotations possible and 4 vibrations possible.
But vibrations contribute RT to the energy
So,
Therefore, has higher internal energy.
(b) Irrespective of the type of the molecule, there are only 3 translation states possible. So, translational kinetic energy is equal to
is equal for both helium and carbon dioxide.
(c) It is known that the ideal gas equation is given as follows.
PV = nRT
Here, it is given that
T is same (same temperature)
n is same (no of moles of gas)
V is same (identical container)
R is a constant.
So, P is equal for both gases.