## T

(b) Express the partial derivatives on the right hand side of this equation in terms of CP and the EOS variables p, v, and T.

6.7 The differentials of the entropy given by Eqs (6.23b) and (6.24b) have a third variant:

ds = Cvfdll dp+Mdll dv

Prove this relationship.

Hint: start with s as a function ofp and v, form its differential, and use the chain rule to convert the partial-derivative coefficients to the desired forms.

6.8 What is the difference between CP and CV (in units of R) for N2 at 300 K and 10 MPa? Nitrogen at these conditions behaves as a Van der Waals gas with constants given by Eq (2.8).

6.9 Show that the equation for the enthalpy change from state 1 to state 2 calculated by the 1-B-2 path in the diagram for the last example in Sect. 6.3.3 is the same as for the 1-A-2 path.

6.10 Show that:

[d v JS Cvpv where P is the coefficient of compressibility. Follow these steps:

1. to obtain an expression for (dp/dv)S:

(a) take the differential of s(p,v)

(b) use divide-and-hold-constant rule

2. To introduce CP and CV, use the chain rule (Eq (6.7))

3. To introduce P, use the cyclic transformation (Eq(6.6))