A. Consider a simple one component system of n moles, with internal energy, U, a

Question

A. Consider a simple one component system of n moles, with internal energy, U, and volume, V. The entropy for the system is given by the relation:

S = S(U,V,n) = U2 V / n

Determine/demonstrate the following relations for:

1. the internal energy U = U(S,V,n)

Are these expressions intensive or extensive?

Hint: To determine these relations first determine the relevant equations of state (obtained as differential relations from the thermodynamic potentials) and then invert these to express each thermodynamic potential in its natural variables. For example, to obtain A = U ? TS as a function A = A(T,V,n), first determine T = T (S,V,n) = (?U ?S)V,n from U = U(S,V,n) and the relation dU = TdS ? PdV + µdn . Then invert T = T (S,V,n) to obtain S = S(T,V,n), which can be used to determine the desired relation for A .

Explanation / Answer

both are extensive properties.

both internal energy (U) and enthaloy (H) are extensive properties.

An extensive property of a substance is a property whose value depends on its quantity.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.