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 4: Not to be turned in or graded (Intended as Practice for Exam 1)

This problem set is designed to simulate the first exam. I expect that each student could answer all the questions in about 45 minutes. You need not turn it in, but I encourage you to compare your answers with your working group. You should study until are satisfied with your answers--this would be much better preparation for the exam than just asking for the answers. Don't expect the TA or the instructor to just tell you the answer. It is also good practice to design your own questions in a similar vein. If you think of a good question that would take 15 minutes to answer and tests something that everyone in the class should know by now, then send it to me; who knows, it may appear on the exam.

Note that the questions ask you to demonstrate your understanding of the lecture material up to and including Lecture 8 on the course calendar--where I expect that we should be by Monday Oct. 2.

When answering questions like these, please think through your response carefully. You may wish to write your answer down on scratch paper and then refine it until you are satisfied with it.

Accuracy is valued above all. Clarity is nearly as important. A brief answer is almost invariably better than an incoherent rambling answer. Furthermore, you should consider that all of your answer will be graded--including the parts that are incorrect.

This is how I intend to grade the exams. For each question, I will read every exam and sort them into about five piles. I will iterate between reading and ranking until I have ranked them according to my best judgment. I will assign points according to the ranking.

Exercise 4.1

The CRC, Handbook of Chemistry and Physics, $58^{\mbox{th}}$ edition, defines the Latent Heat of Vaporization as follows:

The quantity of heat necessary to change one gram of liquid to vapor without change in temperature, measured in calories per gram.

A

As defined, what kind of thermodynamic quantity is the latent heat of vaporization?

B

Suppose you were to measure the latent heat of vaporization of an unknown material. When you report your results to the rest of the world, would you need to augment the CRC definition in any way? If so, be specific.

Exercise 4.2

Consider an ideally linear elastic isotropic body with finite compressibility. The body is a perfect sphere of radius $\ensuremath{{R}_\circ}$ in its unstrained state.

Consider two subsequent processes:

Process A

The body is isothermally and reversibly compressed to a sphere of radius $9\ensuremath{{R}_\circ}/10$. The isothermal compression takes place at $\ensuremath{{T}_\circ}$.

Process B

The body is returned to its unstrained state adiabatically by removing the compressive stress instantaneously.

What predictions can you make about the elastic body after process B? State clearly any important assumptions that you make. Demonstrate how you might quantify any predictions.

Exercise 4.3

For a reversible process, what is the relation between the total heat absorbed by a body during the process and its molar entropy?

What relation holds, if any, for an irreversible process?