13.1Degrees

1
13.1 Degrees
1) one Celsius degree 2) one Kelvin
degree 3) one Fahrenheit degree 4) both one
Celsius degree and one Kelvin degree 5) both
one Fahrenheit degree and one Celsius degree
Which is the largest unit one Celsius degree,
one Kelvin degree, or one Fahrenheit degree?
2
13.1 Degrees
1) one Celsius degree 2) one Kelvin
degree 3) one Fahrenheit degree 4) both one
Celsius degree and one Kelvin degree 5) both
one Fahrenheit degree and one Celsius degree
Which is the largest unit one Celsius degree,
one Kelvin degree, or one Fahrenheit degree?
The Celsius degree and the Kelvin degree are the
same size. The scales only differ by an offset,
not by the size of the degree unit. For
Fahrenheit, there are 180 degrees between boiling
and freezing (212F32F). For Celsius, there
are 100 degrees between the same points, so the
Celsius (and Kelvin) degrees must be larger.
3
13.2 Freezing Cold
1) yes, at 0 C 2) yes, at -273 C 3) yes,
at 0 K 4) no
It turns out that 40C is the same temperature
as 40F. Is there a temperature at which the
Kelvin and Celsius scales agree?
4
13.2 Freezing Cold
1) yes, at 0 C 2) yes, at -273 C 3) yes,
at 0 K 4) no
It turns out that 40C is the same temperature
as 40F. Is there a temperature at which the
Kelvin and Celsius scales agree?
The Celsius and Kelvin scales differ only by an
offset, which is 273 degrees. Therefore, a
temperature on one scale can never match the same
numerical value on the other scale. The reason
that such agreement is possible for Celsius and
Fahrenheit is the fact that the actual degree
units have different sizes (recall the previous
question).
5
13.4 Glasses
1) run hot water over them both 2) put hot water
in the inner one 3) run hot water over the outer
one 4) run cold water over them both 5) break the
glasses

• Two drinking glasses are stuck, one inside the
  other. How would you get them unstuck?

6
13.4 Glasses
1) run hot water over them both 2) put hot water
in the inner one 3) run hot water over the outer
one 4) run cold water over them both 5) break the
glasses

• Two drinking glasses are stuck, one inside the
  other. How would you get them unstuck?

Running hot water only over the outer glass will
allow the outer one to expand, while the inner
glass remains relatively unchanged. This should
loosen the outer glass and free it.
7
13.5a Steel Expansion I
A steel tape measure is marked such that it
gives accurate length measurements at room
temperature. If the tape measure is used outside
on a very hot day, how will its length
measurements be affected?
1) measured lengths will be too small 2)
measured lengths will still be accurate 3)
measured lengths will be too big
8
13.5a Steel Expansion I
A steel tape measure is marked such that it
gives accurate length measurements at room
temperature. If the tape measure is used outside
on a very hot day, how will its length
measurements be affected?
1) measured lengths will be too small 2)
measured lengths will still be accurate 3)
measured lengths will be too big
The tape measure will expand, so its markings
will spread out farther than the correct amount.
When it is laid down next to an object of fixed
length, you will read too few markings for that
given length, so the measured length will be too
small.
9
13.5b Steel Expansion II

• Metals such as brass expand when heated. The
  thin brass plate in the movie has a circular hole
  in its center. When the plate is heated, what
  will happen to the hole?

1) gets larger 2) gets smaller 3) stays the
same 4) vanishes
10
13.5b Steel Expansion II

• Metals such as brass expand when heated. The
  thin brass plate in the movie has a circular hole
  in its center. When the plate is heated, what
  will happen to the hole?

1) gets larger 2) gets smaller 3) stays the
same 4) vanishes
Imagine drawing a circle on the plate. This
circle will expand outward along with the rest of
the plate. Now replace the circle with the
hole, and you can see that the hole will expand
outward as well. Note that the material does
NOT expand inward to fill the hole!!
11
14.1a Thermal Contact I
Two objects are made of the same material, but
have different masses and temperatures. If the
objects are brought into thermal contact, which
one will have the greater temperature change?
1) the one with the higher initial
temperature 2) the one with the lower initial
temperature 3) the one with the greater
mass 4) the one with the smaller mass 5) the
one with the higher specific heat
12
14.1a Thermal Contact I
Two objects are made of the same material, but
have different masses and temperatures. If the
objects are brought into thermal contact, which
one will have the greater temperature change?
1) the one with the higher initial
temperature 2) the one with the lower initial
temperature 3) the one with the greater
mass 4) the one with the smaller mass 5) the
one with the higher specific heat
Since the objects are made of the same material,
the only difference between them is their mass.
Clearly, the object with less mass will be much
easier to change temperature since there is not
much material there (compared to the more massive
object).
13
14.2 Two Liquids

• Two equal-mass liquids, initially at the same
  temperature, are heated for the same time over
  the same stove. You measure the temperatures and
  find that one liquid has a higher temperature
  than the other. Which liquid has a higher
  specific heat?

1) the cooler one 2) the hotter one 3) both
the same
14
14.2 Two Liquids

• Two equal-mass liquids, initially at the same
  temperature, are heated for the same time over
  the same stove. You measure the temperatures and
  find that one liquid has a higher temperature
  than the other. Which liquid has a higher
  specific heat?

1) the cooler one 2) the hotter one 3) both
the same
Both liquids had the same increase in internal
energy, because the same heat was added. But
the cooler liquid had a lower temperature change.
Since Q mcDT, if Q and m are both the same
and DT is smaller, then c (specific heat) must be
bigger.
15
14.3a Night on the Field
The specific heat of concrete is greater than
that of soil. A baseball field (with real soil)
and the surrounding parking lot are warmed up
during a sunny day. Which would you expect to
cool off faster in the evening when the sun goes
down?
1) the concrete parking lot 2) the baseball
field 3) both cool off equally fast
16
14.3a Night on the Field
The specific heat of concrete is greater than
that of soil. A baseball field (with real soil)
and the surrounding parking lot are warmed up
during a sunny day. Which would you expect to
cool off faster in the evening when the sun goes
down?
1) the concrete parking lot 2) the baseball
field 3) both cool off equally fast
The baseball field, with the lower specific
heat, will change temperature more readily, so it
will cool off faster. The high specific heat of
concrete allows it to retain heat better and so
it will not cool off so quickly it has a higher
thermal inertia.
17
14.4 Calorimetry
1) 0 oC 2) 20 oC 3) 50 oC 4) 80 oC 5)
100 oC

• 1 kg of water at 100 oC is poured into a bucket
  that contains 4 kg of water at 0 oC. Find the
  equilibrium temperature (neglect the influence of
  the bucket).

18
14.4 Calorimetry
1) 0 oC 2) 20 oC 3) 50 oC 4) 80 oC 5)
100 oC

• 1 kg of water at 100 oC is poured into a bucket
  that contains 4 kg of water at 0 oC. Find the
  equilibrium temperature (neglect the influence of
  the bucket).

Since the cold water mass is greater, it will
have a smaller temperature change! The masses
of cold/hot have a ratio of 41, so the
temperature change must have a ratio of 14
(cold/hot).
Q1 Q2 m1cDT1 m2cDT2 DT1 / DT2 m2 / m1
19
14.5 More Calorimetry
1) 0oC 2) between 0oC and 50oC 3) 50oC 4)
between 50oC and 100oC 5) 100oC

• A 1 kg block of silver (c 234 J/kg 0C ) is
  heated to 100 0C, then dunked in a tub of 1 kg of
  water (c 4186 J/kg 0C ) at 0 0C. What is the
  final equilibrium temperature?

20
14.5 More Calorimetry
1) 0oC 2) between 0oC and 50oC 3) 50oC 4)
between 50oC and 100oC 5) 100oC

• A 1 kg block of silver (c 234 J/kg 0C ) is
  heated to 100 0C, then dunked in a tub of 1 kg of
  water (c 4186 J/kg 0C ) at 0 0C. What is the
  final equilibrium temperature?

Since cwater gtgt csilver it takes more heat to
change the temperature of the water than it does
to change the temperature of the silver. In
other words, it is much harder to heat the
water!! Thus, the final temperature has to be
closer to the initial temperature of the water.
Q1 Q2 mc1DT1 mc2DT2 DT1 / DT2 c2 / c1
21
14.6 Adding Heat
If you add some heat to a substance, is it
possible for the temperature of the substance to
remain unchanged?
1) yes 2) no
22
14.6 Adding Heat
If you add some heat to a substance, is it
possible for the temperature of the substance to
remain unchanged?
1) yes 2) no
Yes, it is indeed possible for the temperature
to stay the same. This is precisely what occurs
during a phase change the added heat goes into
changing the state of the substance (from solid
to liquid or from liquid to gas) and does not go
into changing the temperature! Once the phase
change has been accomplished, then the
temperature of the substance will rise with more
added heat.
23
14.7 Hot Potato
Will potatoes cook faster if the water is
boiling faster?
1) yes 2) no
24
14.7 Hot Potato
Will potatoes cook faster if the water is
boiling faster?
1) yes 2) no
The water boils at 100 C and remains at that
temperature until all of the water has been
changed into steam. Only then will the steam
increase in temperature. Since the water stays
at the same temperature, regardless of how fast
it is boiling, the potatoes will not cook any
faster.
25
14.8 Water and Ice

• You put 1 kg of ice at 0oC together with 1 kg of
  water at 50oC. What is the final temperature?
• LF 80 cal/g
• cwater 1 cal/g oC

1) 0oC 2) between 0oC and 50oC 3) 50oC 4)
greater than 50oC
26
14.8 Water and Ice

• You put 1 kg of ice at 0oC together with 1 kg of
  water at 50oC. What is the final temperature?
• LF 80 cal/g
• cwater 1 cal/g oC

1) 0oC 2) between 0oC and 50oC 3) 50oC 4)
greater than 50oC
How much heat is needed to melt the ice? Q
m Lf (1000g) ? (80 cal/g) 80,000 cal How
much heat can the water deliver by cooling from
50oC to 0oC? Q cwater m DT (1 cal/g oC) ?
(1000g) ? (50oC) 50,000 cal Thus, there is
not enough heat available to melt all the ice!!
27
14.9 Ice and Steam

• You put 1 kg of ice at 0oC together with 1 kg of
  steam at 100oC. What is the final temperature?
• LF 80 cal/g, Lv 540 cal/g
• cwater 1 cal/g oC

1) between 0oC and 50oC 2) 50oC 3) between
50oC and 100oC 4) 100oC 5) greater than 100oC
28
14.9 Ice and Steam

• You put 1 kg of ice at 0oC together with 1 kg of
  steam at 100oC. What is the final temperature?
• LF 80 cal/g, Lv 540 cal/g
• cwater 1 cal/g oC

1) between 0oC and 50oC 2) 50oC 3) between
50oC and 100oC 4) 100oC 5) greater than 100oC
How much heat is needed to melt the ice? Q
m Lf (1000g) ? (80 cal/g) 80,000 cal How
much heat is needed to raise the water
temperature to 100oC? Q cwater m DT (1
cal/g oC)?(1000g)?(100oC) 100,000 cal But if
all of the steam turns into water, that would
release 540,000 cal. Thus, some steam is left
over, and the whole mixture stays at 100oC.
29
14.12 Heat Conduction
a) a rug b) a steel surface c) a concrete
floor d) has nothing to do with thermal
conductivity

• Given your experience of what feels colder when
  you walk on it, which of the surfaces would have
  the highest thermal conductivity?

30
14.12 Heat Conduction
a) a rug b) a steel surface c) a concrete
floor d) has nothing to do with thermal
conductivity

• Given your experience of what feels colder when
  you walk on it, which of the surfaces would have
  the highest thermal conductivity?

All things being equal, bigger k leads to bigger
heat loss. From the packet Steel50,
Concrete0.8, Human body0.17, Wool0.04, in
units of W/mC0).
31
Three Containers
1) container 1 2) container 2 3) container 3
4) all three are equal

• Three containers are filled with water to the
  same height and have the same surface area at the
  base, but the total weight of water is different
  for each. Which container has the greatest total
  force acting on its base?

32
Three Containers
1) container 1 2) container 2 3) container 3
4) all three are equal

• Three containers are filled with water to the
  same height and have the same surface area at the
  base, but the total weight of water is different
  for each. Which container has the greatest total
  force acting on its base?

The pressure at the bottom of each container
depends only on the height of water above it!
This is the same for all the containers. The
total force is the product of the pressure times
the area of the base, but since the base is also
the same for all containers, the total force is
the same.
33
The Straw I
1) water pressure 2) gravity 3) inertia 4)
atmospheric pressure 5) mass
When you drink liquid through a straw, which of
the items listed below is primarily responsible
for this to work?
34
The Straw I
1) water pressure 2) gravity 3) inertia 4)
atmospheric pressure 5) mass
When you drink liquid through a straw, which of
the items listed below is primarily responsible
for this to work?
When you suck on a straw, you expand your lungs,
which reduces the air pressure inside your mouth
to less than atmospheric pressure. Then the
atmospheric pressure pushing on the liquid in the
glass provides a net upward force on the liquid
in the straw sufficient to push the liquid up the
straw.
35
Wood in Water I

• Two beakers are filled to the brim with water.
  A wooden block is placed in the second beaker so
  it floats. (Some of the water will overflow the
  beaker.) Both beakers are then weighed. Which
  scale reads a larger weight?

1
2
3
same for both
36
Wood in Water I

• Two beakers are filled to the brim with water.
  A wooden block is placed in the second beaker so
  it floats. (Some of the water will overflow the
  beaker.) Both beakers are then weighed. Which
  scale reads a larger weight?

1
2
The block in B displaces an amount of water
equal to its weight, since it is floating. That
means that the weight of the overflowed water is
equal to the weight of the block, and so the
beaker in B has the same weight as that in A.
3
same for both
37
Two Bricks

• Imagine holding two identical bricks in place
  under water. Brick 1 is just beneath the surface
  of the water, while brick 2 is held about 2 feet
  down. The force needed to hold brick 2 in place
  is

1) greater 2) the same 3) smaller
38
Two Bricks

• Imagine holding two identical bricks in place
  under water. Brick 1 is just beneath the surface
  of the water, while brick 2 is held about 2 feet
  down. The force needed to hold brick 2 in place
  is

1) greater 2) the same 3) smaller
The force needed to hold the brick in place
underwater is W FB. According to
Archimedes Principle, FB is equal to the weight
of the fluid displaced. Since each brick
displaces the same amount of fluid, then FB is
the same in both cases.
39
Archimedes I
1) 1/4 2) 1/3 3) 4/3
4) 3/4 5) 2/1

• An object floats in water with 3/4 of its volume
  submerged. What is the ratio of the density of
  the object to that of water?

40
10.12a Archimedes I
1) 1/4 2) 1/3 3) 4/3
4) 3/4 5) 2/1

• An object floats in water with 3/4 of its volume
  submerged. What is the ratio of the density of
  the object to that of water?

Remember that we have so if the ratio
of the volume of the displaced water to the
volume of the object is 3/4, the object has 3/4
the density of water.
41
10.12b Archimedes II
1) it floats just as before 2) it floats higher
in the water 3) it floats lower in the water 4)
it sinks to the bottom

• The object is now placed in oil with a density
  half that of water. What happens?

42
10.12b Archimedes II
1) it floats just as before 2) it floats higher
in the water 3) it floats lower in the water 4)
it sinks to the bottom

• The object is now placed in oil with a density
  half that of water. What happens?

We know from before that the object has 3/4 the
density of water. If the water is now replaced
with oil, which has 1/2 the density of water, the
density of the object is larger than the density
of the oil. Therefore, it must sink to the
bottom.
43
10.15a Fluid Flow

• Water flows through a 1-cm diameter pipe
  connected to a 1/2-cm diameter pipe. Compared to
  the speed of the water in the 1-cm pipe, the
  speed in the 1/2-cm pipe is

(1) one quarter (2) one half (3) the same (4)
double (5) four times
44
10.15a Fluid Flow

• Water flows through a 1-cm diameter pipe
  connected to a 1/2-cm diameter pipe. Compared to
  the speed of the water in the 1-cm pipe, the
  speed in the 1/2-cm pipe is

(1) one quarter (2) one half (3) the same (4)
double (5) four times
The area of the small pipe is less, so we know
that the water will flow faster there. Since A ?
r2, when the radius is reduced by 1/2, the area
is reduced by 1/4, so the speed must increase by
4 times to keep the flow rate (A ? v) constant.
45
On Golden Pond
1) rises 2) drops 3) remains the same 4)
depends on the size of the steel

• A boat carrying a large chunk of steel is
  floating on a lake. The chunk is then thrown
  overboard and sinks. What happens to the water
  level in the lake?

46
On Golden Pond
1) rises 2) drops 3) remains the same 4)
depends on the size of the steel

• A boat carrying a large chunk of steel is
  floating on a lake. The chunk is then thrown
  overboard and sinks. What happens to the water
  level in the lake

Initially the chunk of steel floats by
sitting in the boat. The buoyant force is equal
to the weight of the steel, and this will require
a lot of displaced water to equal the weight of
the steel. When thrown overboard, the steel sinks
and only displaces its volume in water. This is
not so much water -- certainly less than before
-- and so the water level in the lake will drop.