What is the Specific Heat Capacity of Air at 300K and 1 atm?

[hhhmortal]

Homework Statement

What is the the specific heat capacity at constant volume of Air?, with temperature 300k and pressure = 1 atm.

Homework Equations

The Attempt at a Solution

Do I assume that this is a diatomic ideal gas and thus Cv = 5/2 ?


Thanks.

 

[mgb_phys]

Try it and see how close you get to the experimental value ?

Cp = 1003.5 J kg⁻¹ K⁻¹

 

[hhhmortal]

Ok, well I've assumed air is a diatomic gas and that:

Cv = 5/2 R = 20.785

What other equation could I use to work out the precise value of Cv for air?

 

[Mapes]

A few issues with that:

1) "Specific" implies per unit mass, not per mole.
2) Air is a combination of gases, not all of which are diatomic.
3) Air is not a perfectly ideal gas.
4) Additional heat capacity arises from diatomic bond stretching.

Depending on how introductory your thermo class is, issues (2), (3), and (4) may be ignored.

 

[mgb_phys]

Cv = 20.7643 J mol−1 K−1 for air at STP, pretty close to an ideal gas
You could re-calculate it assuming 1% Argon (the major non-diatomic consituent of air) but to account for the difference between the nitrogen and oxygen is a much more complicated model.

 

[hhhmortal]

Ok thanks. I might as well post the whole question because I can't seem to get the right answer.

(Q) Find the thermal conductivity of air under the following conditions:

T = 300 K
pressure = 1 atm
density of air = 1.29 kg/m^-3
coefficient of viscosity is 1.75 x 10-5 Pa.s

Average speed of air molecules is 466 m/s
Mean free path of air molecules is 942 x 10^-10 m


Do I use equation:

Thermal conductivity = [n<v>λ / 3][Cv/6.02 x 10^23]

When I do though, I don't get the correct value...