# (Thermo) Radiation in Cavity. Work and Compression?

1. Nov 16, 2015

### Lagraaaange

1. The problem statement, all variables and given/known data
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?
2. Relevant equations

3. 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)????

2. Nov 16, 2015

### 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.