Thermal energy of a gas in a box

[appplejack]

Homework Statement

What are the factors that determines the thermal energy of a gas in a 3d object like a box

Homework Equations

The Attempt at a Solution

I think thermal energy can be referred to as potential energy and also kinetic energy inside the box. If they are essentially the same, please let me know. I think that determines the thermal energy in the box is temperature, pressure (in terms of how much of gas is compressed - because unlike liquids and solids gases can be compressed.)

 

[Andrew Mason]

Homework Statement

What are the factors that determines the thermal energy of a gas in a 3d object like a box

Homework Equations

The Attempt at a Solution

I think thermal energy can be referred to as potential energy and also kinetic energy inside the box. If they are essentially the same, please let me know. I think that determines the thermal energy in the box is temperature, pressure (in terms of how much of gas is compressed - because unlike liquids and solids gases can be compressed.)

For an ideal monatomic gas,

$$\Delta U = nC_v\Delta T$$

So if one starts at absolute 0 as having 0 internal energy, U would be nCvT. This does not take into account any ground state quantum energies.

For an ideal but not-necessarily monatomic gas, internal energy is:

$$\Delta U = \int_{T_1}^{T_2} nC_vdT$$

Cv may be temperature dependent so it is not necessarily the case that $\Delta U = nC_v\Delta T$.

Internal energy is proportional to temperature which, in turn, is proportional to the average translational kinetic energy of the gas molecules. But this does not mean that internal energy consists only of translational kinetic energy of the gas molecules. For molecules that have internal degrees of freedom (diatomic molecules, for example, can rotate about two axes and vibrate about the centre of mass) some of that internal energy involves not only translational kinetic energy of the centres of mass of the molecules but kinetic energy about the centre of mass of the molecule.

As you point out, molecules can also have potential energy. This is the case with water, for example. Water vapour at 100C has more potential energy than liquid water at 100C.

AM