On Jun 9, 3:43 pm, KMyers1 <KMye...@clearwire.net> wrote:

On Jun 8, 10:50 pm,The_Man<me_so_hornee...@yahoo.com> wrote:

On Jun 8, 8:58 pm, KMyers1 <KMye...@clearwire.net> wrote:

My 25 year old college thermo is a little rusty (well ok, more than a
little). Here are a couple of related problems that I want to solve.
Can anyone tell me how to do it:

1. Have an ideal gas with initial pressure P1, temperature T1, and
volume V1. Now I add a certain amount of heat (measured in kJ or BTU)
without changing the volume (V2=V1). What are the new pressure P2 and
temperature T2?
From the initial conditions and the Ideal gas law, you find the number

of moles of gas (n). The addition of heat will depend on the heat
capacity at constant volume (Cv) for the gas (this will depend on the
number of degrees of freedom from the gas). From Cv/n you will get the
temperature increase dT, so the new temp T2 = T1 + dt.. Then
recalculate the pressure P2 from T2, V, and n

2. Same ideal gas and same initial conditions, but this time I
compress the gas to a new volume V2 in an insulated container. What
are the new pressure P2 and temperature T2?

Use the formula for adiabatic expansion/contration.

P1V1^(gamma)= P2V2^(gamma), where gamma = Cp/Cv.
For an ideal gas, Cp=Cv +R.

I know that I need to use the ideal gas law as part of the solution to
these problems, but that only gives me one equation with two
unknowns. What am I missing for the second equation?

I hope that helps. Simply specficying "ideal gas" isn't enough; you
need to know the number of degrees of freedom for the gas.

Thanks,
Kevin M.- Hide quoted text -

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Very helpful, thanks!

Now a related question. In the problems mentioned above, I am
actually working with real gases rather than ideal. Gases that I am
working with include hydrogen, oxygen, nitrogen, carbon dioxide, and
water vapor. Now I would think that tables giving values for the Cp
and Cv factors that you mentioned would be available online and/or in
reference books. I would also assume (possibly incorrectly) that Cp
and Cv vary with changes in temperature and/or pressure, so that it
isn't accurate to simply assume constant values for Cp and Cv over
wide ranges of temperature and pressure. Therefore, I really need to
find tabular listings of these values over a reasonably wide range of
temperatures and pressures (roughly 0 to 3000 deg F and 0 to 3000
psig), or some way to compute them (possibly from the degrees of
freedom that you mention).

I am not familiar with the concept of degrees of freedom as it relates
to gases, but I would assume from your statement that different gases
have different degrees of freedom, that it is probably somehow related
to their molecular structure, and that Cp and/or Cv can be computed
from that value. So, if you could help me out with some additional
information on where to find Cp and Cv values or how to compute them,
I would certainly appreciate it.

By the way, I already did some searching for Cp and Cv values on the
internet, but all of the values that I am finding so far seem to cover
very limited pressure and temperature ranges. So, either I am
searching wrong, or there must be some kind of assumption or
computation that is generally used which I am missing. Again, I am
guessing that may be related to the degrees of freedom concept that
you mentioned, or possibly these values really don't vary greatly (or
at all?) over large ranges of temperature and pressure?

Thanks again,
Kevin M.

Found a Wikipedia article that pretty well straightens me out
regarding Cv and its dependency on degrees of freedom, etc. Based on
that article, it looks like I should be able to reasonably approximate
Cv as a constant value over the range of temperatures that I'm looking
at for my ballpark purposes. However, I'm still unclear whether Cp
can also be assumed to have a relatively constant value?

Kevin M.- Hide quoted text -

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