# equation to relate pv=nrt to heat capacity of a gas

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Hi

I was wondering if there was some formula that related pv = nrt to the heat capacity of a gas. In other words I would like to find out how much energy a gas has gained if its temperature has gone up (or down) by T

thanks
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Commented:
i know kinetic energy = 3/2nrt but that will only help me for molecules that only have translational motion

Commented:
is it 5/2 nk(t2 - t1)

Commented:
Q = m*c* delta T
m = mass     c = specific heat   Q = energy supplied

Commented:
c at constant volume is different from c at constant pressure

Commented:
are you interested in an ideal gass?    a monoatomic gass     a diatomic gas?

Commented:
for a mon0atomic ideal gas c at constant volume - 3R/2    and c for constant pressure = (5/2)R

Commented:
I have scattered my answer thereby obscuring the ideas. If you use pv = nRt you are dealing with ideal gases.
"I would like to find out how much energy a gas has gained if its temperature has gone up (or down) by T"
Q = n*C* delta T
C = specific heat   Q = energy involved
for a monatomic ideal gas C at constant volume - 3R/2    and C for constant pressure = (5/2)R

C(v) = about 12 for monatomic

Commented:
Hi

I was basically interested in relationship to specific heat capacity and internal energy for ideal and monoatomic/diatomic etc. I already know ideal gas from kinetic energy = 3/2nrt. It was the others I am interested in. I believe i already posted 5/2 nk(t2 - t1 for monoatomic though i wasn't sure if that was the right one

Commented:
how does this relate to pressure...

If you heat a gas in constant volume the temperature will go up according to pv = nrt. The change in the internal energy of the gas that relates to that temperature change can be found from the specific heat capacity of the gas. We have already seen some equations for this in this quesiton for ideal and monoatomic gases.

What if you wanted to look at this from the point of view of pressure and how pressure affects internal energy. I could examine this indirectly by looking at temperature again...If you increase the pressure the temperature will go up. You can find the change in internal energy again from the heat capacity of the gas and teh temperature change. Can you find the change in internal energy from the pressure directly?

Commented:
I am not adding to any answers. I just wanted to give you this link that I just found - see section V:
http://web.mit.edu/16.unified/www/FALL/thermodynamics/thermo_4.htm

But look all around. I think you will enjoy this site. Hit the ? mark icon, and you'll see a thread of Q&A that may interest you, and you see the answer and the statistics of the student's responses.

Also, look at this related link, which I think you will also find interesting:
http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node15.html
Commented:
"
I was basically interested in relationship to specific heat capacity and internal energy for ideal and monoatomic/diatomic etc."
This is a rather broad and unspecific question. A whole tutorial could be written on it (particularly the etc par). Perhaps phoffric's links will be useful.
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"I was basically interested in relationship to specific heat capacity and internal energy for ideal and monoatomic/diatomic etc. "
the relationship to specific heat capacity of what.
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