Assume you have no knowledge about the microscopic information, all you know about the system of pure material is it's equation of state and number of particles. Why can't we get Cv=(∂U/∂T)_{V} from here(if this is wrong how do we solve it?)? Why can we obtained some other quantities just from equation of state(CpCv, (∂U/∂V)_{T} for example)? Is there any fundamental difference between these different types of thermodynamic quantities?
