MASSACHUSETTS INSTITUTE OF TECHNOLOGY

Thermodynamics of Materials

3.00 Fall 2000

W. Craig Carter

Department of Materials Science and Engineering

Massachusetts Institute of Technology

77 Massachusetts Ave.

Cambridge, MA 02139

Problem Set 2: Due Fri. Sept. 22, Before 5PM in 13-5026

Exercise 2.1

Please do problem two of chapter two of Fermi.

Exercise 2.2

Estimate the difference in temperature of water just at the top of Niagra Falls and that just at the bottom.

Exercise 2.3

A closed system is composed of a body of lead and a body of aluminum connected by a wire of gold. The lead sphere has a radius of 0.5 m while the aluminum sphere has a radius of 1 m. The lead body is initially at $300^\circ$C and the aluminum body is initially at $50^\circ$C. The dimensions of the gold wire are 0.1 mm in radius by 10 cm in length at its initial temperature of $200^\circ$C.

Calculate the change in energy of the lead and of the aluminum after the adiabatic system comes to thermal equilibrium. You may ignore the effects of thermal expansion. State any other assumptions that you employ.

Heat capacities at constant pressure
	Molar Heat Capacity	Temperature range	density at $300^\circ$ C	Coefficient of
Material	(joules/(degree mole))	of validity(C)	(g/cm$^3$)	Thermal Expansion
	$\overline{C_p} = a + bT$, $T$ is kelvin			(meter/(meter $^\circ$ C))
Lead	$23.6 + 9.75 \times 10^{-3}T$	$25$ to $325^\circ$ C	$11.34$	$29 \times 10^{-6}$
Aluminum	$20.7 + 12.4 \times 10^{-3}T$	$25$ to $600^\circ$ C	$2.702$	$25 \times 10^{-6}$
Gold	$23.7 + 5.19 \times 10^{-3}T$	$25$ to $1000^\circ$ C	$19.31$	$14.2 \times 10^{-6}$