(Thermo) Radiation in Cavity. Work and Compression?

[Lagraaaange]

Homework Statement

U = u(T)V; P=u(T)/3
a. Find (ds/dt)v and (ds/dv)T in terms of u.
Ans. (ds/dt)v = 1/T[du/dt] and (ds/dv)T = 1/T[du/dv + P]...Correct
b. Show that u(T) = Const*T^4
equate partials above and integrate...Correct
c. Find a Relation between V and T during adiabatic compression or expansion of the cavity?
d. The system goes adiabatically from V1 at T1 to V2. Find work done during expansion in terms of V1, V2,T1?

Homework Equations

The Attempt at a Solution

a. Find (ds/dt)v and (ds/dv)T in terms of u.
Ans. (ds/dt)v = 1/T[du/dt] and (ds/dv)T = 1/T[du/dv + P]...Correct
b. Show that u(T) = Const*T^4
equate partials above and integrate...Correct
c/d?
d. maybe dQ=0=> dW = dU
du = du/dt + du/dv
Plug in and integrate get VU + U(V2-V1)?

 

[Lagraaaange]

Solved C. dU = Vdu + idv then vdu+udv = -pdV integrate and simplify to get: oTV^(1/3) = Const^1/3. Now just need d.