Suppose the following system for a capacitor.(adsbygoogle = window.adsbygoogle || []).push({});

Given: [tex]dE = TdS +\phi dq[/tex]

Where: [tex]\phi[/tex] is the potential and = [tex]\frac{q}{C(T)}[/tex]

Find the heat absorbed in increasing charge from 0 to q. (Capacitance is a function of temp).

So, I get [tex] dF = \phi dq [/tex] and then [tex] F = \frac{q^2}{2C} [/tex]

Next, I tried some Maxwell relations. and got [tex] T\frac{dS}{dq} = T\frac{d\phi}{dT} [/tex].

That didn't get me anywhere because of the C(T) included in phi. So we are still left with a term C'(T) after taking that derivative. Any help out there?

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# Homework Help: Capacitor heat problem (thermo), direction?

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