Midterm Exam 1 for Thermal Physics | PHYS 224, Exams of Thermal Physics

Material Type: Exam; Professor: Cobden; Class: THERMAL PHYSICS; Subject: Physics; University: University of Washington - Seattle; Term: Autumn 2007;

Typology: Exams

Pre 2010

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Page 1 Name _______________________________
Thermal Physics 224 First midterm 9.30 am, Wednesday October 31, 2007
Autumn 2007 Instructor: David Cobden
Do not turn this page until the buzzer goes at 9.30. You must hand your exam to
me by the time I leave the room at 10.25.
Attempt all the questions.
Please write your name on every page and your SID on the first page.
Write all your working on these question sheets. Use this front page for extra working. It is important
to show your calculation or derivation. Some of the marks are given for showing clear and accurate
working and reasoning.
Watch the blackboard for corrections or clarifications during the exam.
This is a closed book exam. No books, notes or calculators allowed.
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Thermal Physics 224 First midterm 9.30 am, Wednesday October 31, 2007 Autumn 2007 Instructor: David Cobden

Do not turn this page until the buzzer goes at 9.30. You must hand your exam to me by the time I leave the room at 10.25.

Attempt all the questions.

Please write your name on every page and your SID on the first page.

Write all your working on these question sheets. Use this front page for extra working. It is important to show your calculation or derivation. Some of the marks are given for showing clear and accurate working and reasoning.

Watch the blackboard for corrections or clarifications during the exam.

This is a closed book exam. No books, notes or calculators allowed.

  1. [4] State the equipartition theorem.
  2. [10] Find an expression for the root mean square speed ݒ௥௠௦ of a dust particle of mass m suspended in air at temperature T.
  3. [6] Find an approximate expression for the root mean square angular velocity ω (^) ୰୫ୱ of the dust particle if its radius is approximately r.
  4. [8] In the course of pumping up a bicycle tire, a volume V 0 of air at atmospheric pressure p 0 is compressed adiabatically to a pressure p 1. Sketch the process on a p-V diagram, indicating also some isotherms. Assume air is an ideal gas.
  5. [8] What is the final volume V 1 of this air after compression? Use ߛൌ 1 ൅ 2/݂ , where f has its usual meaning, and the fact that air is mostly diatomic nitrogen and oxygen.
  1. [4] State the Second Law of Thermodynamics.

12. [6] Show from the definition of entropy S in terms of multiplicity Ω that it is an extensive quantity.

  1. [5] Consider a two-state paramagnet with N dipoles of which q point up. Assume that the paramagnet is completely isolated and the magnetic field is zero, so there is no energy difference between up and down spins. The problem is equivalent to that of finding q pennies with their heads up

in a box of N. What is Ω for the macrostate specified by q?

  1. [4] What is the most probable value of q , assuming that all microstates are equally likely?
  2. [10] Use this, and Stirling’s approximation (݉! ൎ ݉ ݉െ ݉ln ) to find a simple expression for the entropy of the paramagnet when N is large. Demonstrate that it is indeed extensive for this system.