Transcript Physics 106P: Lecture 1 Notes

Temperature and Heat
Temperature Scales
Celcius
Farenheit
Kelvin
212
100
373.15
32
0
273.15
9
F  C  32
5
K  C  273
Water boils
Water freezes
5
C  F - 32
9
C  K - 273
NOTE: K=0 is “absolute zero”, meaning (almost) zero KE/molecule
14
Temp Scales Question

Two cups of coffee are heated to 100 degrees
Fahrenheit. Cup 1 is then heated an additional
20 degrees Centigrade, cup 2 is heated an
additional 20 Kelvin. Which cup of coffee is
hotter?
A) One
B) Two
C) Same
20
Thermal Expansion
 When
temperature rises
molecules have more kinetic energy
» they are moving faster, on the average
consequently, things tend to expand
 amount
of expansion depends on…
change in temperature
original length
Temp: T
L0
Temp: T+T
coefficient of thermal expansion
» L0 + L = L0 +  L0 T
» L =  L0 T (linear expansion)
» V =  V0 T (volume expansion)
L
23
Density Question
As you heat a block of aluminum from 0 C to 100 C
its density
A. Increases
B. Decreases
T = 100 C
C. Stays the same
T=0C
M, V0
r0 = M / V0
M, V100
r100 = M / V100
< r0
26
Example: concrete sidewalk

A concrete (=12x10-6 /K) sidewalk is 10m long when
poured on a cold day (0o C) How much will the length
of the sidewalk increase on a hot day (35o C)?
Example: gas tank

A steel (β=36x10-6 /K) gas tank has a volume of 75 lit.
You fill it up with gasoline (β=950x10-6 /K) early in
the morning when it is cool During the day the
temperature increases by 20o C. How much gas will
spill out?
Differential Expansion Demo
A
bimetallic strip is made with
aluminum =16x10-6 /K on the left, and
iron =12x10-6 /K on the right. At room
temperature, the lengths of metal are
equal. If you heat the strips up, what will
it look like?
A
B
C
Aluminum gets longer, forces curve so its on outside
29
Amazing Water
 Water
is very unusual in that it has a
maximum density at 4 degrees C. That is
why ice floats, and we exist!
1000.00
999.95
999.90
999.85
999.80
999.75
999.70
999.65
999.60
999.55
Density
0
2
4
6
8
10
30
Tight Fit
An aluminum plate has a circular hole cut in it. An aluminum ball (solid
sphere) has exactly the same diameter as the hole when both are at room
temperature, and hence can just barely be pushed through it. If both the
plate and the ball are now heated up to a few hundred degrees Celsius, how
will the ball and the hole fit ?
A. The ball wont fit through the hole any more
B. The ball will fit more easily through the hole
C. Same as at room temperature
35
Why does the hole get bigger when the plate
expands ???
Imagine a plate made from 9 smaller pieces.
Each piece expands.
If you remove one piece, it will leave an “expanded hole”
Object at temp T
Same object at higer T:
Plate and hole both get larger
36
Stuck Lid Question
A glass jar ( = 3x10-6 K-1) has a metal lid ( =
16x10-6 K-1) which is stuck. If you heat them by
placing them in hot water, the lid will be
A. Easier to open
B. Harder to open
C. Same
Copper lid expands more,
making a looser fit, and easier
to open!
38
Heat
 Definition:
Flow of energy between two
objects due to difference in temperature
Note: similar to WORK
Object does not “have” heat (it has energy: temp)
 Units:
Joule
4186 Joules = 1 Calorie = 1000 calories =
calorie: Amount of heat needed to raise
1g of water 1ºC
10
Example: Sears Tower

You decide to take the stairs to the top of the Sears tower (442m).
If you have a weight of 670N and your body was 100% efficient
in converting food into mechanical energy. How many Calories
would you need to eat to replenish your body
Whopper with Cheese: 696 Cal
Big Mac with Cheese:
560 Cal
Specific Heat
 Heat
adds energy to object/system
 IF system does NO work then:
Heat increases internal energy. Q = U
Heat increases temperature!
Q
= c m T
Heat required to increase Temp depends on
amount of material (m) and type of material (c)

Q = cmT : “Cause” = “inertia” x “effect” (just like F=ma)
 cause = Q
 effect = T
 inertia = cm (mass x specific heat capacity)

T = Q/cm (just like a = F/m)
15
Question
 After
a grueling work out, you drink a liter of
cold water (0 C). How many Calories does it
take for your body to raise the water up to
body temperature of 36 C?
1) 36
2) 360 3) 3,600 4) 36,000
1 liter = 1,000 grams of H20
1000 g x 1 calorie/(gram degree) x (36 degree) = 36,000 calories
36,000 calories = 36 Calories!
18
Question
Suppose you have two insulated buckets containing the same amount of water at
room temperature. You also happen to have two blocks of metal of the same mass,
both at the same temperature, warmer than the water in the buckets. One block is
made of aluminum and one is made of copper. You put the aluminum block into
one bucket of water, and the copper block into the other. After waiting a while you
measure the temperature of the water in both buckets. Which is warmer?
1. The water in the bucket containing the aluminum block
2. The water in the bucket containing the copper block
3. The water in both buckets will be at the same temperature
Substance
aluminum
copper
c in J/(kg-C)
900
387
Since aluminum has a higher specific
heat than copper, you are adding more
heat to the water when you dump the
aluminum in the bucket (q=mcT).
20
Specific Heat Question
Suppose you have equal masses of aluminum and
copper at the same initial temperature. You add
1000 J of heat to each of them. Which one ends up
at the higher final temperature
A) aluminum
B) copper
C) the same
Substance
aluminum
copper
iron
lead
human body
water
ice
c in J/(kg-C)
900
387
452
128
3500
4186
2000
T = Q/cm
23
Latent Heat L
 As
you add heat to water, the temperature increases
for a while, then it remains constant, despite the
additional heat!
T
Substance
water
Lf (J/kg)
33.5 x 104
100oC
Lv (J/kg)
22.6 x 105
water
temp
rises
water
changes
to steam
(boils)
steam
temp
rises
Latent Heat
Q added to water
 Latent
Heat L [J/kg] is heat which must be added
(or removed) for material to change phase (liquidgas).
28
Ice Question
 Which
will do a better job cooling your soda, a
“cooler” filled with water at 0C, or a cooler
filled with ice at 0 C.
A) Water
B) About Same
C) Ice
Latent Heat L [J/kg] is heat which must be added
(or removed) for material to change phase (liquidwater
ice
gas).
ice
T
Substance
water
Lf (J/kg)
33.5 x 104
0oC
Lv (J/kg)
22.6 x 105
temp
rises
changes
to water
(melts)
temp
rises
Latent Heat
Q added to water
30
Example: sweat

During a tough work out, your body sweats (and
evaporates) 1 liter of water to keep cool (37 C). How
much water would you need to drink (at 2C) to achieve
the same thermal cooling? (recall CV = 4.2 J/g for water,
Lv=2.2x103 J/g)
33
Question
Summers in Phoenix Arizona are very hot (125 F is not uncommon), and very dry.
If you hop into an outdoor swimming pool on a summer day in Phoenix, you will
probably find that the water is too warm to be very refreshing. However, when you
get out of the pool and let the sun dry you off, you find that you are quite cold for
a few minutes (yes...you will have goose-bumps on a day when the air temperature
is over 120 degrees).
How can you explain this?
35
Example: ice and water
How much ice (at 0 C) do you need to add to 0.5 liters
of a water at 25 C, to cool it down to 10 C?
(L = 80 cal/g, c = 1 cal/g C , cice = 0.5 cal/g C)

Example: ice and water 2

0.8kg of ice (at -10o C) is added to 1.4kg of
water at 20o C, How much of the ice will
melt? (Lf = 33.5x104 J/kg, cwater = 4186 J/kg C,
cice = 2000 J/kg C)
Summary





Temperature measure of average Kinetic Energy of
molecules
Thermal Expansion
L =  L0 T (linear expansion)
V =  L0 T (volume expansion)
Heat is FLOW of energy
Flow of energy may increase temperature
Specific Heat
t = Q / (c m)
Monatomic IDEAL Gas CV = 3/2 R
Diatomic IDEAL Gas CV = 5/2 R
Latent Heat
heat associated with change in phase