Question

Thermodynamic Properties: Two identical, sealed, and well-insulated jars contain different gases at the same temperature. Each container contains the same number of moles of gas. Container 1 contains helium, a monotomic gas with a molecular weight of 4.0 kg/kMol. Container 2 contains CO2, a triatomic linear molecule with a molecular weight of 44 kg/kMol. (a) Which gas has higher internal energy? (b) Which gas has higher translational energy? (c) Which gas has higher pressure?

Answer 1

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 = $\frac{3}{2}RT$

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,

     $U_{He} = \frac{3}{2}RT$

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, $U_{CO_{2}} = \frac{3}{2}RT + \frac{2}{2}RT + 4RT = \frac{13}{2}RT$

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

               $U_{trans} = \frac{3}{2}RT$

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.