Physics 4523, Statistical Physics, Spring 2016
February 10, 2016
_________________________
EXAM 1
Name and Signature
Please do all of the problems. The problems are not all worth equal points. Remember to work each
problem as fully as possible. SHOW ALL WORK as partial credit will be given.
You are allowed one formula sheet only for this test, IT MUST BE IN YOUR OWN HANDWRITING
and you can have items on both sides. You are also allowed a non-programmable calculator. Your name
and signature above indicates that you have obeyed the honor system on this test and have not received or
given aid to or from anyone on this test. Show All Your Work!!!!
2.9979 × 108 m / s
c=
1.38065 ×10−23 J / K =
8.6173 ×10−5 eV / K
kB =
h = 6.6261×10−34 J − s
N avogadro = 6.0221 × 1023 / mole
=
 1.05457148 ×10−34 J − s
1 eV 1.6022 ×10
=
−19
R
=
8.3145 J / mol / K
Joules
1. (5 points). In laymen’s terms, please state the laws of thermodynamics (0th 1st 2nd & 3rd) in their
present form. Please provide, for each law, a grammatical English sentence that accurately states the
law. (Some of the laws have several correct statements – one correct statement is sufficient.)
2. (5 points). Draw a Carnot Cycle on a P-V diagram for an ideal gas. Label each leg of the diagram.
(isobar etc.) and tell how P depends upon V for that leg. Also show the heat taken in, Q1 as well as
the heat exhausted Q2 on the appropriate legs.
3. (10 points). A hot water tank contains 200 kg of water at a temperature of 15 °C = 288 K. The tank
contains an electric immersion heater that produces 10 kW of heating power. Recall the specific heat
of water is 1 cal/gram/ °C = 4.18 kJ / kg / K.
a. How long does it take to heat the water to 70 °C?
b. What is the total entropy change of the water? Give your answer in J/K. You may assume that
heating is slow enough that the water always remains close to equilibrium.
4. (5 points). During a rainstorm, raindrops fall at essentially random time intervals. Suppose that you
place a tin cup in the rain. You notice that the cup catches 12 raindrops per minute, on average.
What is the probability that no more than three drops will fall into the cup during an interval of 15
seconds?
5. (5 points). An apparatus contains five electronic tubes which all have to operate perfectly if it is to
work. If the probability of each tube failing in a two hour period is 0.06, what is the probability that
the apparatus will fail in this interval?
6. (10 points). Suppose that the number of microstates, W, for a system varies as
W = A exp( γ (VU)1/2 )
where V is the volume of the system, U is the internal energy, and A, γ are constants.
a. Find the internal energy U as a function of temperature T.
b. Find an expression for the pressure p that is just in terms of U and V (and constants).