Specific heat at constant pressure


by rabbahs
Tags: specific heat cp
rabbahs
rabbahs is offline
#1
Jan4-11, 01:32 PM
P: 13
Dear Forum members,

I have a bit confusion about the "Specific Heat at constant pressure".

Normally it only varies with the temperature (As given by many book at their Appendixs). But these values are only given at 1 atm pressure and with a wide range of temperature. Most of the books also specify the polynomial related to the specific heat (that only change with temperature, because pressure is held fixed at 1 atm).

My question is that what happen to Cp when the pressure increase from 1 atm to 5 atm at constant temperature. is Cp increase with increase or decrease of pressure ??

I know that its sounds bit odd that asking for Cp (which is indeed sp. heat at CONSTANT PRESSURE)

is there any polynomial which describe the change of Cp with both pressure and temperature ???

Please also view the attached file which clearly shows that Cp is changing with pressure.

I want to know that polynomial having both temperature and pressure.

Thanks alot

Click image for larger version

Name:	nist.jpg
Views:	10
Size:	104.6 KB
ID:	31039
Phys.Org News Partner Engineering news on Phys.org
PsiKick's batteryless sensors poised for coming 'Internet of things'
Researcher launches successful tech start-up to help the blind
Researchers propose network-based evaluation tool to assess relief operations feasibility
Mapes
Mapes is offline
#2
Jan5-11, 09:12 AM
Sci Advisor
HW Helper
PF Gold
Mapes's Avatar
P: 2,532
I don't know if this will get you anywhere, but the change in [itex]C_P[/itex] with pressure is a classic problem in thermo (I remember getting it on an exam before I was familiar with it):

[tex]\left(\frac{\partial C_P}{\partial P}\right)_T=\frac{\partial}{\partial P}\left[\left(T\frac{\partial S}{\partial T}\right)_P\right]_T=T\frac{\partial}{\partial P}\left[\left(\frac{\partial S}{\partial T}\right)_P\right]_T=T\frac{\partial}{\partial T}\left[\left(\frac{\partial S}{\partial P}\right)_T\right]_P[/tex]

Then we use a Maxwell relation to get

[tex]T\frac{\partial}{\partial T}\left[\left(-\frac{\partial V}{\partial T}\right)_P\right]_P=-T\left(\frac{\partial^2 V}{\partial T^2}\right)_P[/tex]

Thus, the change you're looking for is related to the second derivative of volume with temperature. This is zero for an ideal gas, but it may get you somewhere if you have a constitutive equation for a real gas.
rabbahs
rabbahs is offline
#3
Jan5-11, 01:10 PM
P: 13
thanks Mapes, i will look it to these equations and let you know

rabbahs
rabbahs is offline
#4
Jan5-11, 01:33 PM
P: 13

Specific heat at constant pressure


could you kindly give me the reference of the book in which these relations related to specific heat are discussed ??
Mapes
Mapes is offline
#5
Jan7-11, 12:45 PM
Sci Advisor
HW Helper
PF Gold
Mapes's Avatar
P: 2,532
Actually, nearly every thermodynamics book will define specific heat and explain Maxwell relations. Zemansky is pretty good.
rabbahs
rabbahs is offline
#6
Jan8-11, 12:28 AM
P: 13
thanks


Register to reply

Related Discussions
Specific Heat Capacity - high pressure gas Materials & Chemical Engineering 6
specific heat capacity at constant pressure General Physics 1
high pressure gases specific heat Materials & Chemical Engineering 1
Specific Heat Constant Volume Question Classical Physics 6
Constant Volume Specific Heat Introductory Physics Homework 4