## Info

(a) Starting from the fundamental differentials for du and dh, derive expressions for (du/dp)T and (du/dT)p in terms of CP and the equation-of-state variables a, P and v. Use Maxwell's equations where needed.

(b) what temperature change (at 1 atm) produces the same change in internal energy as a pressure increases from 1 atm to 100 atm? The specific heat of the solid is 400 J/kg-K,

T = 300 K and the p-v-T properties of the substance are: density = 8.8 g/cm3; a = 5x10- K- ; P = 9x10- MPa- . Assume that the density is independent of p and T.

(c) Express (dh/dv)T in terms of the EOS variables a and p.

6.3 One kg of a solid is compressed reversibly from p1 to p2 at a fixed T. Calculate:

(a) the work required.

(b) the heat exchanged in maintaining constant T

(c) the change in the internal energy

6.4 A gas obeying the Van der Waals EOS is compressed from specific volume v1 to v2 at constant temperature. Derive the equations for the changes in u, h, and s for this process. What do these reduce to for an ideal gas?

6.5 A gas obeying the Van der Waals equation of state is initially at pressure p1 and specific volume v1. It undergoes an isentropic expansion to p2 = 0.1 MPa.

(a) What is the equation giving the final specific volume, v2?

(b) For N2 initially at v = 2.5x10-4 m3/mole and 10 MPa, calculate the ratio v2/v1 by:

(i) The full Van der Waals formula (i.e., the equation derived in part (a))

(ii) The Van der Waals formula with the constant a = 0

(iii) The ideal gas law (both a and b equal to zero)

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