(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)

Solar Panel Basics

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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