Temperature and HeatTemperature and Heat

Temperature ScalesTemperature Scales

Water boils

Water freezes

212

32

Farenheit

100

0

Celcius

273.15

373.15

Kelvin

273-K C 273 C K

32-F9

5 C 32 C

5

9 F

NOTE: K=0 is “absolute zero”, meaning (almost) zero KE/molecule14

Temp Scales QuestionTemp 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

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Thermal ExpansionThermal 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 temperatureoriginal lengthcoefficient of thermal expansion

» L0 + L = L0 + L0 T

L = L0 T (linear expansion)

V = V0 T (volume expansion)

Temp: T

Temp: T+T

L0

L

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Density QuestionDensity QuestionAs you heat a block of aluminum from 0 C to 100 C its density

A. Increases

B. Decreases

C. Stays the same T = 0 C

M, V0

0 = M / V0

T = 100 C

M, V100

100 = M / V100

< 0

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Example: concrete sidewalkExample: 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 tankExample: 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 DemoDifferential 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 WaterAmazing Water

Water is very unusual in that it has a maximum density at 4 degrees C. That is why ice floats, and we exist!

999.55

999.60

999.65

999.70

999.75

999.80

999.85

999.90

999.95

1000.00

0 2 4 6 8 10

Density

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Tight FitTight FitAn 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

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Why does the hole get bigger when the plate expands ???

Object at temp TSame object at higer T:

Plate and hole both get larger

Imagine a plate made from 9 smaller pieces. Each piece expands. If you remove one piece, it will leave an “expanded hole”

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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

Stuck Lid QuestionStuck Lid Question

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Copper lid expands more, making a looser fit, and easier to open!

HeatHeat

Definition: Flow of energy between two objects due to difference in temperatureNote: similar to WORKObject does not “have” heat (it has energy: temp)

Units: Joule4186 Joules = 1 Calorie = 1000 calories =calorie: Amount of heat needed to raise

1g of water 1ºC10

Example: Sears TowerExample: 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 HeatSpecific Heat Heat adds energy to object/system IF system does NO work then:

Heat increases internal energy. Q = UHeat increases temperature!

Q = c m THeat required to increase Temp depends on amount

of material (m) and type of material (c) Q = cmT : “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

QuestionQuestion 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

QuestionQuestionSuppose 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

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=mcT). 20

Substance c in J/(kg-C)aluminum 900copper 387

Specific Heat QuestionSpecific Heat QuestionSuppose 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) aluminumB) copperC) the same

T = Q/cm

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Substance c in J/(kg-C)aluminum 900copper 387iron 452lead 128human body 3500water 4186ice 2000

Latent Heat L Latent Heat L As you add heat to water, the temperature increases

for a while, then it remains constant, despite the additional heat!

Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid-gas).

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T

Q added to water

water temp rises

water changesto steam

(boils)

steam temp rises

100oC

Latent HeatSubstance Lf (J/kg) Lv (J/kg)

water 33.5 x 104 22.6 x 105

Ice QuestionIce 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

T

Q added to water

ice temp rises

ice changesto water(melts)

water temp rises

0oC

Latent HeatSubstance Lf (J/kg) Lv (J/kg)

water 33.5 x 104 22.6 x 105

Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid-gas).

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Example: sweatExample: 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

QuestionQuestionSummers 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?

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Example: ice and waterExample: 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 2Example: 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)

SummarySummary Temperature measure of average Kinetic Energy of

molecules Thermal Expansion

L = L0 T (linear expansion)V = L0 T (volume expansion)

Heat is FLOW of energyFlow of energy may increase temperature

Specific Heatt = 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