Free energy per unit volume of an ideal gas

[Pushoam]

Homework Statement

Homework Equations

The Attempt at a Solution

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I am taking the free energy as the internal energy of the ideal gas.

Then the average internal energy per unit volume is $\frac { 3 nk_B T } {2 }$.

So, the correct option is (c).

Is this correct?

 

[Useful nucleus]

I am taking the free energy as the internal energy of the ideal gas.

Why did you introduce this approximation?

Also could you let us know the source of these questions.

 

[Pushoam]

Why did you introduce this approximation?

Also could you let us know the source of these questions.

I didn't introduce it thinking that this is an approximation. I thought that free energy is another name for internal energy.
But, now I think that the free energy should be another name for kinetic energy as kinetic energy gives an idea of the particles's freedom to move.
For an ideal gas, the internal energy is defined as the average kinetic energy of the molecules.

I think here, free energy should be the kinetic energy of the whole macrscopic system i.e. gas and I was approximating this kinetic energy of the macroscopic system to the average kinetic energy of the constituent gas molecules unknowingly as this was the only thing which I could do.

The source of these questions is the JNU ( An Indian University) Entrance Exam 2013 for M.Sc.Physics.

 

[rude man]

Free energy F = U - TS
U = internal energy
S = entropy

You need to invoke the 1st law and the entropy, both of an ideal gas, to come up with the answer.