(2) The natural independent variables for U are (S,V), from dU = TdS – pdV. U = U (S, V)=gives simple expressions for T and p as Tinstead. Show that U =(24) ²and P: ==where f(V) is an unknown function of V.U (V, T) leads to a much more complicated expression for p, namelydTF = S (2 V ) , I/7/71T²au(). Suppose you use (V,T)S+ ƒ(V),

The first law of thermodynamics is

(2) The natural independent variables for U are (S,V), from dU = Tds - pdV. U = U (S,V) gives simple expressions for I and p as T = (35), and p = - (3). Suppose you use (V, T) instead. Show that U = U (V,T) leads to a much more complicated expression for p, namely au dT F = f (OV), II + f(V). S (2V)₁ T T² T where f (V) is an unknown function of V.

(2) The natural independent variables for U are (S,V), from dU = Tds - pdV. U = U (S,V) gives simple expressions for I and p as T = (35), and p = - (3). Suppose you use (V, T) instead. Show that U = U (V,T) leads to a much more complicated expression for p, namely au dT F = f (OV), II + f(V). S (2V)₁ T T² T where f (V) is an unknown function of V.