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(physicsPhDQualifyingExamination)[2008](s)final~ph_wdg^_10522.pdf
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Department of Physics, HKUST
PhD Qualifying Examination (Morning Session)
9:30 am C 12:00 pm, 25 October 2008

Instructions:
1. Be sure that your identification number (not your name!) is written on the cover page of the Examination Answer Book.

2. Begin each question on a new page. Write down the corresponding question number at the top of each page.

3. Answer 6 out of 8 questions. Only 6 questions will be used to calculate your final grade. If you answer more than six questions and do not indicate your choice of questions, the lowest scores will be used.

4. The examination time is 2.5 hours. All questions carry the same amount credits. You should budget your examination time carefully and accordingly.

5. Some questions are composed of more than one part. It is not always necessary to successfully complete one part in order to do the other parts.

6. Grades on the examination will be determined, in part, by such things as the clarity and organization of the response C the use of written statements between the lines of an algebraic proof, etc. Be sure to substantiate any answer by calculations or arguments (in complete sentences), as appropriate. Be concise, explicit, and complete.

7. The use of simple electronic calculators is permitted. However, obtaining preprogrammed information from programmable calculators, using tables, books, papers, or any other reference material that is not provided by the exam committee, or any other form of cheating is strictly prohibited and punishable according to the UST regulations on academic dishonesty.




1. As shown in the figure below, a thick round cylindrical shell of mass M is rolling over a planar surface without slipping, having a center-of-mass velocity v. Find its kinetic energy.





2. (a) One kilogram of water at 0C is in contact with a large heat bath at 100C. When the water temperature has increased to 100C, how much does the entropy change for the water, and how much does the entropy change for the whole system? (Useful information: the specific heat of water is c = 4.18 J/g.)
(b) If more than one heat bath is available, describe a thermodynamic process which will reduce the entropy change for the whole system when the water is heated from 0C to 100C.
(c) If relativity effects are considered, does the mass of water change when it is heated from 0C to 100C? If yes, how much is the mass change .m? If not, briefly explain your reasons in a few sentences.


3. Consider a rectangular glass rod with a horseshoe shape, as shown in the figure below. A parallel light beam falls perpendicularly on the flat surface A. Determine the minimum value of the ratio R/d for which all light entering the glass through the surface A will reach the surface B through the glass rod. The index of refraction of the glass is 1.5.





4. The energy-band diagram of an isolated metal and an isolated semiconductor is