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Re: Thermo problem help!



Regarding Ken Fox's plea for help:

I can use some help.

I am building a worksheet to show the difference in isothermal and
adiabatic expansion. Using Q = dU + W as first law. For adiabatic dU = -W.
Plotting the process on a PV diagram I used P*V^gamma = constant. For air
gamma = 1.40....according to one reference.

Now I calculate dU (really it is deltaU) as = 1.5nR(T2 - T1).

Oops. You have an inconsistency here. If you take gamma to be 1.4
then you are not allowed to take DU = 1.5*n*R*DT. If you want to use
the diatomic gamma value of 7/5 then the coefficient of the DU
expression needs to be 2.5 = 5/2, not the 1.5 = 3/2 you have above.
You seem to be using a DU for a monatomic gas while doing adiabatic
work on a diatomic one. The numerical coefficient of the DU
expression is supposed to be 1 / ([gamma] - 1).

The the work
should be the area bounded by the PV graph (I hope). The problem is that
for the numbers I am using dU and W do not agree.
P1 = 200 kPa ; V1=1 m^3; n = 0.04 mol; T1 = 600K
P2 = 103 kPa ; V2 = 1.6 m^3; n = 0.04 mol ; T2 = 496K
delta U = -51 J area under graph (counting squares ) 88J

I am sure I am missing something important or have a gross misconception.
Can anyone help?

Thanks in advance!

Ken Fox

Try it again using a 2.5 coefficient in the DU expression. That
ought to fix the problem.

David Bowman