# Thermal Physics and Differentials

A hypothetical substance has a compressibility k = a /V and a volume expansivity
B = 2bT /V , where a and b are constants and V is the molar volume. Show that the
equation of state is:
V = bT2 - aP + constant

To be honest I'm not entirely sure what I'm actually supposed to be doing with this question. Do I treat it as an ideal gas and therefore use that equation or is that completely wrong.

So far I have integrated each of the equations in respect to T, giving me,

(integral of) a/V dT = aT/V + c

(integral of) 2bT/V dT = bT^2/V + c

But now I'm stuck and can't seem to find a relevant relationship between P and what I've got there.

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vela
Staff Emeritus
Homework Helper
Your first equation is wrong. Compressibility has to do with the change in volume due to a change in pressure, not temperature.

So do I integrate both in terms of dP?

vela
Staff Emeritus
Homework Helper
Both what?

What are the (mathematical) definitions of compressibility and expansivity?

Well I think they're k = 1/P and B = 1/T but I've been given equations for both in the question.

vela
Staff Emeritus
Homework Helper
Sorry, I meant the general definitions in terms of derivatives.

To be honest I really don't know. I've become very confused with all the derivatives and general definitions.

vela
Staff Emeritus