Thermo physics. Dealing with adding dQ to a system with P held constant.

[oexnorth]

"Measured heat capacities of solids and liquids are almost always at constant pressure, not constant volume. To see why, estimate the pressure needed to keep V fixed as T increases, as follows.
a)First imagine slightly increasing the temp of a material at constant pressure. Write the change in volume, dV1, in terms of dT and the thermal expansion coefficient Beta."
There's more to it, but I'll start with just this for now.



Beta=deltaV/(VdeltaT), PV=NkT,



It says to write in terms of dT and Beta, but I am having a hard time trying to get rid of V when I rearrange as dV1=Beta*V*dT. I am missing something here, I just need a push in the right direction.

 

[oexnorth]

Anybody?

 

[Mapes]

Your equation is correct; the question should have included V.

 

[oexnorth]

Thank you. But if it tells me to write v1 in terms of dt and Beta, then doesn't that mean I have to get rid of the V term?

Here's some more equations, I don't know if it will help.

Specific heat is C
Q is heat added or lost to the system
deltaU is the change in internal energy of the system
partialX is the partial derivative of a variable.
W is the work done on the system
Cp is C under conditions of constant pressure
C=Q/deltaT=(deltaU-deltaW)/deltaT
Cp=partialU/partialT+P(partialV/partialT)

Thanks again.

 

[Mapes]

You've got to have the system size somewhere in the equation, as $dT$ and $\beta$ are both intensive properties.

Another option is to call $dV$ the normalized change in volume, so it's just a number.