Physics 4C: Collected Homework 2
Solutions are not considered complete without the logical argument and/or full calculation.
1. A sturdy aluminum canteen is filled to the very top with 2.00 L of water at 5◦ C. If
the temperature increases to 90◦ C, how much water overflows the canteen? (Volume
halliday_c18_476-506v2.qxd 22-10-2009 12:03 Page
506
coefficients of thermal expansion: water 6.9 × 10−5 ◦ C−1 , aluminum 2.3 × 10−5 ◦ C−1 .)
HALLIDAY
2. Figure (a) shows a cylinder containing 5.00 moles of an ideal gas and closed by a
movable piston. The cylinder is kept submerged in an ice-water mixture. A cycle of
3 steps is completed: (A) the piston is very quickly pushed down from position 1 to
position 2, and then (B) held at position 2 until the gas is again at the temperature of
the ice-water
then (C) it is slowly raised back to position 1. Figure (b) is a
506 mixture,
CHAPTER
18 TEMPERATURE, HEAT, AND THE FIRST LAW OF THER
P -V diagram for the process. The volume of the cylinder with the piston in position
1 is 4 times the volume with the piston in position 2 (V1 = 4V2 in figure (b)).
86 A glass window pan
80 Figure 18-55a shows a cylinder containing gas and closed by a
(a) If
100 g of
ice is melted
during
thesubmerged
cycle, howinmuch
hasmixbeen done
the has its area inc
howon
much
movable
piston.The
cylinder
is kept
an icework
– water
gas?
suming that it can expand
ture. The piston is quickly pushed down from position 1 to position 2
and
then
held
at
position
2
until
the
gas
is
again
at
the
temperature
of
(b) What is the work done on the gas in step (A)? (Hint: Think about87
the A
other
recruit can join
the ice – water mixture; it then is slowly raised back to position 1.
steps.)
Amundsen – Scott South
Figure 18-55b is a p-V diagram for the process. If 100 g of ice is
perature is below !70°C.
(c) What is the heat transferred to the gas in step (B)?
melted during the cycle, how much work has been done on the gas?
hot sauna and then runs
course, extremely danger
against the constant dang
Assume that upon st
temperature is 102°F and
1
room have a temperature o
and take the skin emissivi
net rate Pnet at which the re
2
Ice and
changes with the room? N
water
Start
cruit’s surface area exchan
perature of !25°C and th
with the snow and ground
V2
V1
proximate net rate at whic
Volume
tion exchanges with (b) the
(b)
(a)
Pressure
** View All
Solutions Here **
Fig. 18-55
88 A steel rod at 25.0°C
At what temperature will
Problem 80.
p
81 SSM A sample of gas undergoes a transition from an initial
state a to a final state b by three 3pi/2
different paths (processes), as
shown in the p-V diagram in Fig.
p
a
2
1
89 An athlete needs to l
ing iron.” (a) How many ti
tance of 1.00 m in order to
much fat is equivalent to
every 2.00 s, how long does
The opposite ends of the
are in thermal contact w
energy reservoirs at diffe
temperatures.
3. Consider two rods of metal with the same cross sectional area, and the same length.
The two rods have different thermal conductivities.
L
Energy
transfer
Th
(a) Suppose the two rods are welded end to end, as shown in figure a, with a temper- Th ! Tc
Insulation
ature of Tc on the right side and Th on the left side. Derive an expression (don’t
just write it down!) for the total heat transfer rate (power transfer) between
Figure two
20.12 Conduction of en
uniform,
insulated rod of lengt
surfaces at temperatures Th and Tc , (Th > Tc ) across the two rods. Let athe
thermal conductivity of the first rod be k1 and the second be k2 , the length of the
Therefore, the rate of energy transfer by conduct
rods be L, and the cross sectional area be A.
Th 2 Tc
(b) Suppose Tc = 0◦ C and Th = 100◦ C. When the rods are in the configuration shown
P 5 kA a
L
in figure a, 10 J is conducted at a constant rate from the left side to the right side
in 2.0 min. How much time would be required to conduct
10 J if the rods were
For a compound slab containing several mater
welded side to side between the same reservoirs, as thermal
in figureconductivities
b?
k , k , . . . , the rate of en
steady state is
Th
Rod 1
Rod 2
1
2
P5
Tc
A 1 Th 2 Tc 2
a 1 L i /k i 2
i
where Th and Tc are the temperatures of the ou
stant) and the summation is over all slabs. Examp
results from a consideration of two thicknesses of
a
Rod 1
Th
Rod 2
Tc
b
Figure 20.13
(Quick Quiz 20.5)
In which case is the rate of energy
transfer larger?
Q uick Quiz 20.5 You have two rods of the same
formed from different materials. The rods are
different temperatures so that energy transfers
can be connected in series as in Figure 20.13a
In which case is the rate of energy transfer by h
when the rods are in series. (b) The rate is larg
(c) The rate is the same in both cases.
4. A space probe that has travelled very far from the Earth and Sun and is now in deep
Example
Transfer
Through
Slabs
space. It has a 100 W thermal
energy20.8
source. Energy
The surface
of the
probeTwo
is perfectly
2
black and has an area of 6.0 m . The power source is internal to the space probe.
(a)
(b)
Two slabs of thickness L 1 and L 2 and thermal conductivities k 1 and k 2 are in
thermal
contact with
shown as
in Figure
20.14.above?
The temperatures of
What is the (steady state) temperature
ofeach
the other
spaceasprobe
described
their outer surfaces are Tc and Th , respectively, and Th . Tc . Determine the temWhat is the steady stateperature
temperature
of the and
space
a thin
thermal
shield through
at the interface
theprobe
rate of if
energy
transfer
by conduction
an space
area A probe?
of the slabs
in shield
the steady-state
condition.
(also black) surrounds the
The
is attached
close to the probe’s
surface by a number of thermally insulating supports. Between the shield and the
SOLUTION
probe’s surface is a vacuum.
(Hint: this thermal shield is a simple example of
multi-layer insulation that
is
often
used
on spacecraft.
Think
about howcondition.”
the shieldWe interpret
Conceptualize
Notice
the phrase “in
the steady-state
itself will absorb and emit
this radiation.)
phrase to mean that energy transfers through the compound slab at the
same rate at all points. Otherwise, energy would be building up or disappearing at some point. Furthermore, the temperature varies with position in the two
slabs, most likely at different rates in each part of the compound slab. When the
system is in steady state, the interface is at some fixed temperature T.
Categorize We categorize this example as a thermal conduction problem and
impose the condition that the power is the same in both slabs of material.