Thermodynamics: Isothermal Compressibility and Expansivity Equations

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The discussion focuses on solving problems related to isothermal compressibility and expansivity equations for a hypothetical substance. The user successfully solved part of the problem but struggles with evaluating the constant in the equation of state. They attempted to substitute known values for specific volume, temperature, and pressure but are uncertain about the correctness of this method. The user also seeks clarification on using exact differential equations in this context. Additionally, there is a request for assistance with formatting the kappa symbol in their post.
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Homework Statement



Hi, I got a set of problems to do and there are a few I am having trouble with: (edit: I had more questions before but I figured them out)

1. A hypothetical substance has an isothermal compressibilty \kappa=a/v and an expansivity \beta=2bT/v, where a and b are constants, and v is the specific volume.
a) Show that the equation of state is given by v-bt2 + aP=constant
b) If at a pressure P0 and temperature T0, the specific volume is v0, evaluate the constant.



The Attempt at a Solution



1. Ok I figured out 2a), but I don't know how to evaluate the constant for 2b)...what I did was just replace v, T, and P with v0, t0, and P0, but I don't think that is right.

I think it may be something with an exact differential equation, I am not sure though. I have (\beta\nu/\partialP)\partialT = -(\kappa\nu/\partialT)\partialP
Help for that one please



Btw how do you make the kappa symbol on the same level as everything else?
 
Last edited:
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Ok number 3 I figured out
 
Any help?
 

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