# Thermal Physics > Air and Internal Energy

#### Ivegottheskill

This Q has me stumped, I'm still flicking through some web pages and my text book, but been unable to find a useful formula to work it out yet:

What is the internal energy U of one mole of air on a very hot summer day (35C)?

In answering the questions in this problem, assume that the molecules in air (mainly N2 and O2) have five degrees of freedom at this temperature (three translational and two rotational).

Related Introductory Physics Homework Help News on Phys.org

#### jdstokes

Ivegottheskill said:
This Q has me stumped, I'm still flicking through some web pages and my text book, but been unable to find a useful formula to work it out yet:

For each molecule, the kinetic energy associated with each degree of freedom is $\frac{1}{2}kT$, so the kinetic energy of each molecule in the O2, N2 mixture is $\frac{5}{2}kT$. Summing over the entire gas gives the internal energy $U = N\frac{5}{2}kT = nN{_\mathrm{A}} \frac{5}{2}kT = \frac{5}{2}nRT$.

P.S. Not PHYS1901 by any chance?

#### Ivegottheskill

No. PHYS 1001 actually
I just found this forum, looks like a useful resource all round.

Thanks for clearing that up. My main problem I think is remembering all the letters and where they come from.

BTW, you have U = N*5/2*k*T = n*N_a*5/2*k*T

The only thing that changes there is N --> n*N_a

What is "N" if N=n*N_A

(Haven't worked out how to use the "Latex" code yet)

#### jdstokes

$k$ is defined as $\frac{R}{N_\mathrm{A}}$, N is the number of gas molecules.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving