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**PHY 3513 Fall 1999 – Sample Mid-Term Exam 1**

*Answer all four questions, which carry equal weight. To obtain full credit, please explain your reasoning and show all working. Please write neatly and include your name on the front page of your answers.*

**You must not seek or obtain help on this exam from anyone other than the instructor, nor must you assist anyone else.**

1. One liter of gas with

*γ*

= 1

*.*

3 is initially at 273 K and 1.0 atm pressure. It is suddenly

(adiabatically) compressed to half its original volume.

(a) Find the final temperature and pressure of the gas.

(b) Find the work done on the gas during the compression process.

Take

*R*

= 8

*.*

31 J/(mol

*·*

K).

2. Consider the three fundamental relations below:

*(i) u*

=

*Rθv v*

0 exp(

*− s/R*

*); (ii) s*

*= u*

*θ exp( v/v*

0

*); (iii) u*

= s s 3

*R v*

*0 v*

*θ exp( s/R*

)

*.*

Determine whether each of the fundamental equations satisfies the fundamental entropy postulates.

3. A closed system is composed of two simple subsystems, labeled

A and

*B*

.

A is a simple ideal gas, described by

*S*

*A*

=

*N*

*A s*

0

+

*N*

*A*

R ln

"

*U*

*A*

*U*

*0 c V*

*A*

*V*

0

*N*

0

*N*

A c +1

#

*,*

(1) and

B is a cavity containing electromagnetic radiation described by

*S*

*B*

=

4

3 b U 3

*B*

*V*

*B*

1 / 4

*.*

(2)

Initially the subsystems are separated by an adiabatic, rigid, impermeable barrier.

Then the barrier is replaced by one that is diathermal, rigid, and impermeable.

(a) Write an equation for

*U*

A,f initial temperatures

*T*

A, 0

, the final internal energy of

*A*

, as a function of the and

*T*

B, 0 , and of constants introduced in Eqs. (1) and

(2).

*(Do not attempt to solve this equation.)*

(b) Write

*U*

*B,f*

,

*T*

*A,f*

, and

*T*

B,f in terms of

*U*

*A,f*

,

*T*

A, 0

,

*T*

B, 0

, and constants.