EF 152 – Physics for Engineers
Fall, 2010
Recitation 3.7 Review 1
1. A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water and the
other end in a water-ice mixture. The rod has a uniform cross-sectional area of 4.36 cm2 and a
length of 82 cm. The heat conducted by the rod melts the ice at a rate of 1 gram every 22
seconds. What is the thermal conductivity of the rod?
[ 284 W/(m°C)
2. How many grams of ice at -23°C must be added to 176 grams of water that is initially at a
temperature of 69ºC to produce water at a final temperature of 8ºC? Assume that no heat is lost
to the surroundings and that the container has negligible mass.
[ 108g ]
3. A closed, 7.10-L tank contains argon at 33°C and absolute pressure of 9.0x105 Pa, How much
energy is required to raise the temperature of the argon gas to 62°C? Assume that argon is an
ideal monatomic gas.
[ 908 J ]
4. If a certain sample of an ideal gas has a temperature of 145°C and exerts a pressure of 8.7x104 Pa
on the walls of its container, how many gas molecules are present in each cubic cm of volume?
[ 1.5x1019 ]
5. One mole of helium is in contact with a thermal reservoir at 350K and is under 10 atm of
pressure. The pressure is slowly increased to 25 atm. (a) What are the initial and final volumes of
the gas? (b) How much work is done by the gas? (c) What is the change in internal energy of the
gas? (d) What is the heat flow into the gas?
[ Vi=0.00287m3; Vf = 0.00115m3; W=-2661J; ΔU=0; Q=-2661J ]
6. In an engine where the process is modeled by an Otto cycle, the working fluid is an ideal
monatomic gas, with =1.7, At the beginning of the adiabatic power stroke, the temperature of
the hot gas is 260°C and at the end of the power stroke (just before the exhaust stroke), the
temperature of the cooler gas is 27°C. What is the compression ratio of this engine?
[ 2.3 ]
7. A Carnot heat engine operates between reservoirs at TH = 1650 K and TC = 150K. In each cycle,
490 J of heat energy is rejected to the low temperature reservoir. In each cycle, how much
mechanical work W is performed by the engine?
[ 4900 J ]
8. A Carnot refrigerator takes heat from water at 0°C and rejects heat to a room at 12°C Suppose
that 92 grams of water at 0°C are converted to ice at 0°C by the refrigerator. Calculate the
mechanical energy that must be supplied to the refrigerator.
[ 1350 J ]
Equation sheet on other side.
Use any remaining time to answer questions about on-line homework.
EF 152 Exam #3, Spring, 2010
Name:
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Section: ________
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• Assume 3 significant figures for all given numbers .
• Show all of your work – no work, no credit
• Write your final answer in the box provided - include units for all answers..
• If you finish with less than 5 minutes remaining, remain seated until the end of the exam and
all exams are collected.
Thermal Expansion
Linear
Work of Thermal Systems
Linear, Stresses
Isobaric (constant pressure)
Volumetric
Heat
Q– heat
c – specific heat
κ – thermal conductivity
R – thermal resistance
Heat Capacity
Ideal Gas Law
Isochoric (constant volume)
Thermal Conductivity
R = 8.314 J/(mol-K)
23
Avogadro’s Number: 6.02x10
Isothermal (constant temp)
Thermal Resistance
Standard Pressure and Temp
273K 1.00 atm (101.3kPa)
Thermal Resistance, Series
st
1 Law of Thermodynamics
U – internal energy
W – work done by thermal
system
Q – heat flow into thermal
system
Molecular Thermal Physics
m – mass of a molecule
M – molecular mass
n – number of moles
N – number of molecules
k – Boltzmann constant =
-23
1.38065 × 10 J/ K
Adiabatic (ΔQ = 0)
Efficiency
General
Otto Cycle
r – compression ratio
Thermal Resistance, Parallel
Refrigerators
General
K – coefficient of performance
H – heat current
P – power input
Carnot Cycle
Carnot
Entropy
Ideal Gas
Conversions
1 cal = 4.186 J
3
1 L = 1000 cm
3
1 m = 1000 L
Water Properties
c = 1 cal/(g-°C) = 4.186J/(g-°C)
Lf = 79.6 cal/g
Lv = 540 cal/g
3
ρ = 1 g/cm = 1 kg/L
3
3
= 1000 kg/m = 62.4 lb/ft
Lf = Latent heat of fusion
Lv = Latent heat of vaporization
Standard Pressure and Temp
273K 1.00 atm (101.3kPa)