I have a question about Equation 45.17 in the Feynman Lectures on
Physics. Feynman is applying thermodynamics to photons and has chosen
to treat T and V as independent variables and to treat U(T,V) and P(T,V)
as dependent variables. He takes the partial derivative of U=3PV (comes
from equation 39.17) holding T constant and obtains:
dU/dV (const T) = 3P
I was expecting:
dU/dV (const T) = 3P + 3V dP/dV (const T)
Why is the second term missing? Its absence would suggest that P(T,V)
is actually only a function of T, P(T). Equation 39.18, PV^(4/3)=C
(where C is a constant), would lead one to believe that P is indeed a
function of V.