Thermal/statistical physics:
a gas of interacting particles has an equation of state and heat capacity at constant volume given by the expression:
p(v, t)=a_{1}t^\frac{5}{2}+a_{2}t^3 +a_{3}v^-2 , c_{v}(t, v)=b_{1}vt^\frac{3}{2}+b_{2}t^2v+b_ {3}t^\frac{1}{2} where ai and bi are constants independent of t and v
find:
1.) the differential of internal energy in terms of dt and dv.
2.) the relationship between (some of) ai and bi due to the fact that u(t, v) is a function of state.
3. ) u(t, v) as a function of t and v.