Thermodynamic Properties: Two identical, sealed, and well-insulated jars contain different gases at the same temperature. Each c

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Thermodynamic Properties: Two identical, sealed, and well-insulated jars contain different gases at the same temperature. Each c

ontainer 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?

Physics

1 answer:

Ostrovityanka [2.2K] · Answer 1 · 2026-03-22T08:01:13+03:00

Clarification:

Assuming the gas behaves as an ideal gas in this scenario.

(a) Thus, the formula for the internal energy of a monoatomic gas can be described as follows.

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

In the case of a monoatomic ideal gas, there are three types of translational motion, which means there is no rotational motion.

According to the equipartition principle, internal energy can be affected by every form of translational, rotational, or vibrational motion present in the system.

Specifically for Helium, which qualifies as a monoatomic ideal gas,

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

For carbon dioxide, a linear triatomic molecule, the possible states include 3 translational motions, 2 rotational motions, and 4 vibrational motions.

However, vibrations add RT to the energy

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

This leads to having greater internal energy.

(b) Regardless of molecular structure, there are only 3 types of translational movements possible. Thus, the kinetic energy associated with translation is expressed as

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