Thermal Physics > Air and Internal Energy

[Ivegottheskill]

This Q has me stumped, I'm still flicking through some web pages and my textbook, 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).

 

[jdstokes]

This Q has me stumped, I'm still flicking through some web pages and my textbook, 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 [itex]\frac{1}{2}kT[/itex], so the kinetic energy of each molecule in the O2, N2 mixture is [itex]\frac{5}{2}kT[/itex]. Summing over the entire gas gives the internal energy [itex]U = N\frac{5}{2}kT = nN{_\mathrm{A}} \frac{5}{2}kT = \frac{5}{2}nRT[/itex].

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]

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