Physics 221: Exam III, Spring-lO
Name:
Section. No:
NOTE: Each problem is worth 20 pts
1. Consider the following two-step process. Heat is allowed to flow out of an ideal gas at constant
volume so that its pressure drops from 2.2 atm to 1.4 atm. Then the gas expands at constant pressure,
from a volume of 5.9 L to 9.3 L, where the temperature reaches its original value.
NOTE: 3
Pa,andlL=10
5
latm=l.OlxlO
c
m
a) Sketch this process on a P-V diagram
b) Calculate the total work done by the gas in the process.
c) The change in internal energy of the gas in the process
d) The total heat flow into or out of the gas
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-
a bo b
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2. When a gas is taken from a to c along the curved path, the work done by the gas is W = -35 J and the
heat added to the gas is is Q = -63 J. Along the path abc, the work done is W = -54 J.
a) What is Q for path abc?
,/2, what is W for path cda?
1
b) If P = P
cj
—
c) What is Q for path eda?
d)WhatisAUca?
e) IMUa
= 12 J, what is Q for path da?
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3. A copper rod and an aluminum rod of the same length and cross-sectional area are attached end-to-end. The
copper end is placed in a furnace maintained at a constant temperature of 225°C. The aluminum rod is placed in
an ice bath held at constant temperature of 0.0°C. Calculate the temperature at the point where the two rods are
joined. (NOTE: Thermal conductivities are: kAJ = 200 J/(m-s-C°),
= 380 J/(m-s-C°)).
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L
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A
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225
S.C
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4. The operation of a certain heat engine takes an ideal monatomic gas on a cycle shown below. NOTE: In this
problem all results an be expressed in terms of P
0
0 and V
a) Calculate the net work W done by the system
b) Calculate Qab,
Qcd, Qth, and then the net heat Q entering the system
c) Compute the efficiency for this engine
d) Compare (as a ratio) the efficiency of this engine to that of a Carnot engine operating between TH and T,
where TH and T are the highest and lowest temperatures achieved.
1
rc
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5. Consider an isolated gas-like system consisting of a box that contains N = 10 distinguishable atoms,
each moving at the same speed v. The number of unique ways these atoms can be arranged so that NL
atoms are within the left-hand half of the box and NR atoms are within the right-hand half of the box is
given by N!/(NR!NL!) where the! is the factorial symbol and 0! = 1. Defme each unique arrangement of
atoms within the box to be a microstate of this system. Now consider the following two macrostates:
state A where all of the atoms are within the left-hand half of the box and none are in the right-hand
half; and state B where there is the same number in each half. Note: k = 1.38 x 1023 j,i
a) Assume the system is initially in state A and, at a later time, is found to be in state B. Determine the
system’s change in entropy.
b) Can this process occur naturally?
c) Now assume the system is initially in state B and, at a later time, is found to be in state A. Determine
the system’s change in entropy.
d) Can this process occur naturally?
State A (NL
10, NRO)
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State B (NL =5, NR = 5)
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