The fundamental equation of classical thermodynamics for a single component system can be expressed by a first order homogeneous equation: U=U(S,V,N) (iv) Write an expression for the differential, dU, in terms of the appropriate partial derivatives of U. [Mark: 2 percent] (v) Link these partial derivatives to the conjugate intensive parameters associated with each extensive parameter. [Mark: 4 percent] (vi) Using the first order homogeneous property of the fundamental equation of classical thermodynamics U(S,V,N), show that the three conjugate intensive parameters, T,P and μ, are not independent (i.e. derive the Gibbs-Duhem relationship).