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 5: Due Fri. Oct. 27, Before 5PM in 13-5026
(Two Weeks, but don't procrastinate)

Exercise 5.1

(Be careful, this question is a little tricky.)

Calculate the minimum number of joules per cubic meter required to heat a room of ideal monatomic gas from 10${}^\circ$C to 20$^\circ$C at constant atmospheric pressure.

Exercise 5.2

Consider heating a body $A$, of constant heat capacity $1$J/${}^\circ$C and initially at temperature 100K, to a final temperature of 200K. The heating takes place by sequentially placing it in thermal contact with $N$ different large thermal reservoirs (so large that there temperature does not change during thermal contact).

For example,

$N$=1

The body $A$ is placed in contact with a single reservoir at 200K.

$N$=2

The body $A$ first attains thermal equilibrium with a one reservoir at $T$=150K; subsequently, it attains thermal equilibrium with the second at $T$=200K.

$N=M$

The body $A$ first attains thermal equilibrium with a one reservoir at $T= (100 + 100/M)$K. Next, it attains equilibrium with a reservoir at $T= (100 + 2{\times}100/M)$K. $\ldots$. Next, it attains equilibrium with a reservoir at $T= (100 + j{\times}100/M)$K. $\ldots$. Finally, $A$ attains equilibrium with a reservoir at $T= (100 + M{\times}100/M)$K.

On the same graph, plot the change in (1) entropy of the body $A$ and (2) the change in entropy of the universe as a function of $1/N$.

Exercise 5.3

Consider a closed system of 1 microgram of solid lead initially at 273K and constant atmospheric pressure. The system receives heat isochorically and isobarically at a rate of 1 millicalorie per decifortnight from a gigagiant thermal reservoir at 2000K.

Lead melts at 327.502${}^\circ$C and boils at 1740${}^\circ$C. The molar latent heat of melting for lead at 1 atm is 4.81 kilojoules. Use as a standard reference state for entropy and enthalpy, $\ensuremath{\overline{\ensuremath{{H}^{\mbox{solid}}}}}(T=273\mbox{K, }P=1\mbox{atm}) = 0$ and $\ensuremath{\overline{\ensuremath{{S}^{\mbox{solid}}}}}(T=273\mbox{K, }P=1\mbox{atm}) = 0$.

Heat capacity of Pb at constant 1 atm pressure
Phase	Molar Heat Capacity	Temperature range
	$\overline{C_p} = a + bT$, $T$ is kelvin	(Kelvin)
Solid	$23.6 + 9.75 \times 10^{-3}T$	298-600
Liquid	$32.4 - 3.1 \times 10^{-3}T$	600-2013

Plot the following as a function of time.

1. The entropy of the universe.
2. The entropy of the lead.
3. The phase fractions of liquid and solid lead.
4. The enthalpy of the lead.
5. The molar entropy of the liquid lead.
6. The molar entropy of the solid lead.
7. The molar enthalpy of the liquid lead.
8. The molar enthalpy of the solid lead.
9. The Gibbs free energy of the lead.
10. The Gibbs free energy of the liquid lead.
11. The Gibbs free energy of the solid lead.
12. The molar Gibbs free energy of the liquid lead.
13. The molar Gibbs free energy of the solid lead.

Exercise 5.4

Write a Haiku poem about the second law of thermodynamics. Haiku is a three line poem, the first and third line each have five and the second line has seven syllables. Haiku quality is judged not only by beauty and subtlety of expression but also on the density of meaning and content.

If you wish your Haiku to be added to the incipient website:
http://pruffle.mit.edu/3.00/Literature_of_Thermodynamics/. Please email it to me (ccarter@mit.edu) and it will be included in the public collection and attributed to you.