- #1
grandpa2390
- 474
- 14
Homework Statement
I didn't have enough space to make the topic any more precise. Here is the full question:
Express the Internal Energy with Internal Pressure.
Homework Equations
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This is what I know:
the internal pressure is (dU/Dv)T
the fundamental equation for internal energy is dU = T*dS - P*dV
The third Maxwell relation: (dP/dT)v = (dS/dV)t
Cv = (dU/dT)v
The Attempt at a Solution
dividing by dV and imposing the constant T, then using the third Maxwell relation, we arive at
(dU/dV)t = T*(dP/dT)v - P
then I am supposed to consider the internal energy as a function of T and V.
dU(T,V) = (dU/dT)v*dT + (dU/dV)t*dV
this is where I come to my issue. Through google I found that (dU/dV)t *dV is -P
I can't find anything that gives me the relationship between T*(dP/dT)v and (dU/dT)v*dT
I know that (dU/dT)v is the Constant volume heat capacity. but I don't understand the transition... if that makes sense. I don't understand how those two terms are equivalent.