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Quiz #9
PHYSICS 101
Nov 28, 2001
1)A quantity of 1.2 moles of Helium, an ideal monatomic gas with gamma=Cp/Cv=5/3, at a pressure
of 2x105 N/m2 and temperature of 380 K first undergoes an isothermal expansion until its volume is
doubled and then undergoes an adiabatic expansion until its temperature is half the original value.
Recall that R=8.31 J/mole K
a) What is the volume at the end of the isothermal expansion? (2 pt)
b) What is the volume at the end of the adiabatic expansion? (2 pts)
(CONTINUED ON OTHER SIDE)
Rewrite and sign the honor pledge: “I pledge my honor that I have not violated the Honor
Code during this examination.”
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c) What is the net amount of work done by the gas in the two processes? (3 pts)
d)What is the net heat added to the gas for both processes? ( 2 pts)
2) The temperature of an ideal gas is doubled from 250 K to 500 K. What is the fractional increase in
the rms velocity of the atoms? (1 pt)
Physics 101 Quiz #9
November 27, 2002
Name
20 Minutes. Box your answers.
J
R = 8.31 mole
K
kb = 1.38 × 10−23
1 atm = 1.013 × 105 mN2
J
K
NA = 6.02 × 1023
particles
mole
1. 20.9 J of heat is added to an ideal gas. As a result, the gas volume changes from
50.0 to 100.0 cm3 while the pressure remains constant at 1.00 atm.
(a) [3 points] By how much did the internal energy of the ideal gas change?
(b) [3 points] What is the molar specific heat capacity for this (constant
pressure) process if 2.00 × 10−3 moles of the gas are present? (Note: the
gas may or may not be monatomic.)
(c) [1 points] Is the gas monatomic? (Justify your answer.)
Continued on the other side....
2. [3 points] Suppose that you have a mixture of xenon, Xe, (molecular mass
131.1 u) and argon, Ar, (molecular mass 39.9 u). Assume that each behaves as
an ideal monatomic gas and determine the rms speed of the Xe and Ar molecules
when the temperature is 293 K.
Rewrite and sign the honor pledge: “I pledge my honor that I have not violated the
Honor Code during this examination.”
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Physics 101 Quiz #9
December 5, 2003
Name
20 Minutes. Box your answers.
Problem 1
100 moles of an ideal monoatomic gas undergo a reversible thermodynamical cycle,
as shown in the P V diagram below:
5
3
x 10
Pressure (Pa)
2.5
A
2
B
1.5
1
0.5
0.5
C
D
1
1.5
2
2.5
Volume (m3)
a → b: isothermal expansion; b → c: adiabatic expansion;
c → d: isobaric compression; d → a: isochoric process
Ta = Tb = 300 K, Va = Vd = 1 m3 , Pc = Pd = 105 Pa, Vc = 2 m3 .
(Gas constant R = 8.31 J/(mol · K))
(a)[1 point] Find the temperature Tc .
(b)[2 points] Find the internal energy Ub of the gas at point b.
Continued on the other side....
(c)[5 points] Fill in the table (fill in all entries that do not have an ‘X’) by computing
the change in internal energy, the work done by the gas and the heat added to the
gas in each step. Note that ∆U , W and Q can be positive, negative or zero. (Write
your answers in formulas before plugging in the numbers).
∆U
a→b
b→c
c→d
d→a
Wa→b
W
= 9 · 104 J
X
X
Q
X
X
(a→b)
(d) [2 points] What is the change in entropy ∆Sgas of the gas in going from a to b?
(a→b)
What is the change in entropy ∆Suniverse of the universe in going from a to b?
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Honor Code during this examination.”
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Physics 101 Quiz #9
December 3, 2004
Name
20 Minutes. Box your answers.
Data: R= 8.31 J/(mol K); atomic mass of neon= 20.18 u; 1 atmosphere = 1.013×10 5
Pa.
Problem: A container with 50.00 grams of neon, an ideal monoatomic noble gas,
undergoes a three part process. In part 1, it is heated so that the gas gradually
expands from an initial state A with volume VA = 0.1 m3 to a final state B with
volume VB = 0.5 m3 , at constant atmospheric pressure. In part 2, the gas undergoes
an isochoric (constant volume) decompression to state C. In part 3, it returns from
C to A isothermally.
1. [2 points] Schematically plot this cycle on the PV graph below (you need not
calculate exact values for unknown quantities yet).
P(Pa )
1.0
0.5
0.1
0.2
0.3
0.4
0.5
V(m 3)
2. [2 points] Find the volume VC , the pressure PC and temperature TC at point C.
Continued on the other side....
3. [2 points] Find the work done, the heat absorbed and the change in internal
energy in part 1.
4. [2 points] Find the work done, the heat absorbed and the change in internal
energy in part 2.
5. [2 point] Find the change in entropy during the isothermal compression (part
3).
Rewrite and sign the honor pledge: “I pledge my honor that I have not violated the
Honor Code during this examination.”
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QUIZ 9
Physics 101, Fall 2005
Throughout, please box your answers! You have 20 minutes to complete the quiz.
Problem 1: Hurricanes
One of the driving mechanisms in a hurricane is the heat engine arising from cool air (cold
reservoir) moving over warm waters (hot reservoir). For a variety of reasons, hurricanes only
occur if the ocean surface temperature is above 27 ◦ C, or approximately 80◦ F.
a.) If the temperature difference between the surface water and the air at the top of a
hurricane is 10 C◦ , what is the maximum possible efficiency for a hurricane heat engine
moving over water at a temperature of 27 ◦ C? [1 pt]
b.) Assuming that the kinetic energy of the wind in a hurricane comes from the work done by
a heat engine with the efficiency found in (a), how much heat is extracted from the ocean for
each mole of air accelerated to the minimum wind speed of a category-1 hurricane (74 mph,
or 119 km/hr)? Hint: the molar mass of air is 29 g/mol. [3 pts]
c.) What is the change in entropy of the ocean due to the heat loss found in (b)? (Assume
the ocean temperature remains constant.) [2 pts]
QUIZ 5
Physics 101
Problem 2: Carnot Refrigerator
The inside of a Carnot refrigerator is kept at −10 ◦ C, while the temperature in the kitchen
is 19 ◦ C.
a.) What is the coefficient of performance for this refrigerator? [2 pts]
b.) How much heat is exhausted into the kitchen while the refrigerator converts 100 g of
water at 19 ◦ C to ice at −10 ◦ C? (Hint: cwater = 4186 J/(kg C◦ ), cice = 2000 J/(kg C◦ ) and
Lf = 33.5 × 104 J/kg.) [2 pts]
Rewrite and sign the pledge: I pledge my honor that I have not violated the Honor Code during
this examination.
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