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Heat Capacity

Heat Capacity- the amount of heat required to raise

the temperature of an object by 1C.

This definition applies only to objects that are made

of a mixture of several substances. Pure substances,

like distilled water possess another property.

Specific Heat Capacity- The amount of heat

required to raise the temperature of 1g of a substance

by 1C. The specific heat capacity of a substance is a

characteristic physical property that is it is always the

same for any amount of that substance.

A formula can be used to find the energy needed to

heat 1g of a specific substance by 1C.

E = mcT

Where E is the energy in Joules, m is the mass of the

substance, and T is the change in temperature. ( is

a Greek symbol called delta and it means change in)

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Latent Heats

Latent Heat is the amount of heat involved in a state change. It is “hidden heat” since

the energy involved does not result in a change in temperature.

There are 2 types of latent heat:

1. Specific Latent Heat of Fusion (lf)

2. Specific Latent Heat of Vaporization (lv)

Specific Latent Heat of Fusion (Lf)

Melting or Freezing

This is the amount of heat required to melt 1g of a substance with no change in

temperature. Recall there is no temperature change during the melting process, as the

potential energy is increasing not the kinetic energy.

******** Latent Heat of Fusion Value for water is 333 J/g *******

This means at 0C it takes 333J of energy to melt 1g of ice. On the other hand 1g of

water will give off 333J of energy when it freezes.

Formula used for Melting and Freezing:

E = m lf

Where lf = latent heat of fusion (333J/g)

m = mass (g)

E= quantity of energy (J)

Example: How much heat is required to melt 3g of ice cubes placed in a food cooler?

Specific Latent Heat of Vaporization (Lv)

Boiling or Condensing

This is the amount of energy required to vaporize 1g of a substance with no temperature

change.

********Latent Heat of Vaporization for water is 2,260J/g*******

This means that at 100C it takes 2,260 Joules of energy to vaporize 1g of water. On the

other hand, 1g of steam condensing into liquid water releases 2,260J of energy.

Formula used for Vaporizing or Condensing:

E = m lv

Where lv = latent heat of vaporization (2,260J/g)

m= mass (g)

E = energy (J)

Example: How much heat is required to vaporize 2.5kg of water at 100C?

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Latent Heat Explains a number of Natural Phenomena: (note question 7-11 at

multiple step problems. It is important to look at what temperature you are starting

from and finishing at. Then look on the heating curve of water to see how many

steps are involved.)

1. Why does putting ice cubes in water make your drink cold? (Consider the law of

conservation of energy).

2. Our bodies naturally sweat. Why does this cool us?

3. Gardeners often spray their crops before a frost. This prevents the products from

freezing. Explain.

4. Which is better at keeping food in a cooler cold, 10kg of ice at 0C or 10kg of water

at 0C? why?

5. How much heat is given off when 2kg of water at 0C freezes into ice at 0C?

6. How much heat is needed to change .06kg of water at 100C into steam at 100C?

7. Calculate the total heat required to melt .1kg of ice at -20C. (the final temperature

will be 0C) How many steps? _______

8. Calculate the quantity of heat needed to convert .05kg of ice initially at -10C into

water at 80C? How many steps? _______

9. Calculate the minimum amount of heat needed to vaporize 4kg of water at 80C.

How many steps? _______

10. How much heat is released when 150g of steam at 130C is condensed and cooled to

30C? How many Steps? _______

11. Calculate the heat needed to convert .08kg of ice at -40C to steam at 160C.

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Heat Capacity Worksheet

1. Brianna is stocking shelves when she notices smoke coming from another part of the store, when she

reaches the back door she finds the temperature of the door has risen 50ºC. If the door has a mass of

10,000g and the fire has generated 225,000J of energy, what material is the door made of?

2. Travis is heating up a 12,500g piece of metal with a torch, and the torch is giving off 15,000J of

energy. The temperature of the metal rises 3.15ºC what is the metal Travis is heating?

3. Brittany is stirring the soup she just bought at the cafeteria, she notices that her spoon has gotten 5

degrees warmer. Her spoon has a mass of .008kg and has absorbed 50J of energy. What is the specific

heat capacity of the spoon?

4. Joel is burning ants with a magnifying glass and is applying 200J of energy to the ants whose

temperature rises 60ºC. If the ants have a mass of 1g what is the specific heat capacity of the ants?

5. Nicole wants to cool her coffee down by 10ºC. If she has 1kg, of coffee and the coffee loses 40,000J

of energy what is the specific heat capacity of the coffee?

6. Chris fills a 500g glass with very cold soda. If the specific heat capacity of glass is .840J/gºC and the

temperature of the glass drops 15ºC how much energy did the glass lose?

7. Justin is melting .453kg of snow in his hands as he makes a snowball (which he shouldn’t be doing).

Since the SHC (specific heat capacity) of ice is 2.1J/gºC and the ice experiences a temperature change

of 6 degrees how much energy was given to the snow by Justin?

8. Tyrone is soldering two wires together, to do this he must raise the temperature of the wires by 70ºC.

If the wires have a mass of .034kg and are made of copper how much energy must he apply to the

wires?

9. Glissel. is trying to heat up her room from 15ºC to 20ºC, to do this she must heat the air in her room. If

there is 27kg of air in her room, how much energy is needed to heat the room?

10. Brendan is sick and running a fever, if Brendan heat capacity is 3.00J/gºC and his temperature has

gone up 4ºC how much energy has been used? (Brendan has a mass of 80kg)

11. Breanna is boiling water to make Kraft Dinner; if she applies 60,000J of energy to 1.4kg of water how

much does the temperature increase by?

12. Nathaniel is photocopying some papers, the photocopier gives off 28J of energy to each sheet of paper,

(mass = .01g). If the specific heat capacity of paper is 1.800J/gºC how much does the temperature of

paper increase after it is copied?

13. Chassidy is warming her hands after coming in from outside, if her heat capacity is .310J/gºC and her

hands have a mass of 2kg and 2480J of energy are used how much does the temperature of her hands

increase?

14. When the space shuttle lifts of 200,000,000J of energy are transferred to the launch pad. If the pad is

made of concrete and has a mass of 500,000kg what is the temperature increase of the launch pad?

15. Halogen lamps generate 3000J of energy; if the base of the lamp is made of lead and has a mass of 1.8

kg how much does the temperature of the base increase?

16. Kara is making Ichiban so she must heat water from 50-100ºC. If she uses 1,000,000J what mass of

water is she heating?

17. A block of iron is heated by 465J of energy, which raises its temperature by 14ºC, what is the mass of

the block?

18. To make french fries vegetable oil must be heated from 20ºC to 85ºC if this takes 50,000J of energy

what is the mass of the oil?

19. On a hot day the temperature of a concrete sidewalk increases by 12ºC if this required 3,000,000J what

is the mass of the sidewalk?

20. A silver spoon is being used to stir a very hot meal. If the temperature is increased from 20ºC to 49ºC

and 400J of energy was used what is the mass of the spoon?

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Science 10 Specific Heat Capacities Chart

Substance

Aluminum

Brick

Concrete

Copper

Glass

Gold

Human Body (Average)

Ice

Iron

Lead

Protein

Rock

Sand

Silver

Wood

Alcohol (ethyl)

Alcohol (Methyl)

Glycerine

Mercury

Vegetable Oil

Water

Air (Atmospheric)

Carbon Dioxide

Helium

Hydrogen

Nitrogen

Oxygen

Steam

Specific Heat Capacity

(J/gºC)

.900

3.000

2.900

.390

.840

.130

3.470

2.116

.460

.130

1.700

.880

.800

.230

1.760

2.300

2.500

2.400

.140

2.000

4.200

.995

.836

5.250

14.400

1.040

.916

2.020

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Specific Heat Review

1. Jamie L. is heating up a pipe to use on a sink. He uses 18720J of energy and the temperature of the

pipe rises 120ºC and the mass of the pipe is 1.2kg, what is the pipe made of? Gold or Lead

2. Scott is heating 2.3kg of an unknown liquid. He adds 322000J of energy and the temperature increases

from 10ºC to 80ºC. What is the unknown liquid? Vegetable Oil

3. Neil is heating 3.4 kg of an unknown metal. By adding 129948J of energy he is able to raise the

temperature from 22ºC to 120ºC, what is the metal? Copper

4. Karina is at the beach and falls asleep. When she fell asleep the temperature of the sand was 24ºC,

when she wakes up the temperature is 77ºC. If the mass of the sand around her is 180kg, how much

energy did the sand absorb? 7632J

5. Kristin is heating the helium inside a hot air balloon. The helium has a mass of 10kg and increases in

temperature by 67ºC. How much energy was used? 3517500J

6. Brittany is walking barefoot on a skating rink. The ice under her feet has a mass of 2.2kg and

increases from –8ºC to 0ºC. How much energy was lost from Brittany’s feet? 37241.6J

7. Mike puts on a ring made of silver that has an initial temperature of 5ºC. The temperature soon

reaches 37ºC; this required 384J of energy. What is the mass of the ring? 52.2g

8. Sandra has coffee in a glass. The temperature of the glass increases from 20ºC to 65ºC, because the

coffee transferred 22680J of energy to it. What is the mass of the glass? 630g

9. Some cars have brake lines made of brass. Brake fluid can get very hot, if the brake fluids increases

the temperature of a brake line by 91ºC by giving it 56784J of energy what is the mass of the brake

line? 1560g

10. What is the temperature increase of a concrete sidewalk with a mass of 200kg exposed to 1,000,000J

of energy? 1.7ºC

11. A spoon is being used to stir soup. The spoon has a mass of .2kg and is made of silver. If 5, 000J are

transferred to it how much will its temperature increase? 109ºC

12. The outlet of a flame-thrower is made of aluminum, and has a mass of .5kg. The

flamethrower produces 250,000J of energy, if the initial temperature of the outlet is

18ºC what is the final temperature? 573.5ºC

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Heat Capacity Worksheet

1. Brianna is stocking shelves when she notices smoke coming from another part of the store, when

she reaches the back door she finds the temperature of the door has risen 50ºC. If the door has a

mass of 10,000g and the fire has generated 225,000J of energy, what material is the door made of?

Iron 2. Travis is heating up a 12,500g piece of metal with a torch, and the torch is giving off 15,000J of

energy. The temperature of the metal rises 3.15ºC what is the metal Travis is heating? Copper

3. Brittany is stirring the soup she just bought at the cafeteria, she notices that her spoon has gotten 5

degrees warmer. Her spoon has a mass of .008kg and has absorbed 50J of energy. What is the

specific heat capacity of the spoon? 12.5J/gºC

4. Joel is burning ants with a magnifying glass and is applying 200J of energy to the ants whose

temperature rises 60ºC. If the ants have a mass of 1g what is the specific heat capacity of the

ants? 3.3J/gºC

5. Nicole wants to cool her coffee down by 10ºC. If she has 1kg, of coffee and the coffee loses

40,000J of energy what is the specific heat capacity of the coffee? 4J/gºC

6. Chris fills a 500g glass with very cold soda. If the specific heat capacity of glass is .840J/gºC and

the temperature of the glass drops 15ºC how much energy did the glass lose? 6300J

7. Justin is melting .453kg of snow in his hands as he makes a snowball (which he shouldn’t be

doing). Since the SHC (specific heat capacity) of ice is 2.1J/gºC and the ice experiences a

temperature change of 6 degrees how much energy was given to the snow by Justin? 5708J

8. Tyrone is soldering two wires together, to do this he must raise the temperature of the wires by

70ºC. If the wires have a mass of .034kg and are made of copper how much energy must he apply

to the wires? 928.2J

9. Glissel. is trying to heat up her room from 15ºC to 20ºC, to do this she must heat the air in her

room. If there is 27kg of air in her room, how much energy is needed to heat the room? 134,325J

10. Brendan is sick and running a fever, if Brendan heat capacity is 3.00J/gºC and his temperature has

gone up 4ºC how much energy has been used? (Brendan has a mass of 80kg) 960,000J

11. Breanna is boiling water to make Kraft Dinner; if she applies 60,000J of energy to 1.4kg of water

how much does the temperature increase by? 10.2ºC

12. Nathaniel is photocopying some papers, the photocopier gives off 28J of energy to each sheet of

paper, (mass = .01g). If the specific heat capacity of paper is 1.800J/gºC how much does the

temperature of paper increase after it is copied? 1555.6ºC

13. Chassidy is warming her hands after coming in from outside, if her heat capacity is .310J/gºC and

her hands have a mass of 2kg and 2480J of energy are used how much does the temperature of her

hands increase? 4ºC

14. When the space shuttle lifts of 200,000,000J of energy are transferred to the launch pad. If the pad

is made of concrete and has a mass of 500,000kg what is the temperature increase of the launch

pad? .13ºC

15. Halogen lamps generate 3000J of energy; if the base of the lamp is made of lead and has a mass of

1.8 kg how much does the temperature of the base increase? 12.8ºC

16. Kara is making Ichiban so she must heat water from 50-100ºC. If she uses 1,000,000J what mass

of water is she heating? 4761g

17. A block of iron is heated by 465J of energy, which raises its temperature by 14ºC, what is the

mass of the block? 72.2g

18. To make french fries vegetable oil must be heated from 20ºC to 85ºC if this takes 50,000J of

energy what is the mass of the oil? 384.6g

19. On a hot day the temperature of a concrete sidewalk increases by 12ºC if this required 3,000,000J

what is the mass of the sidewalk? 86,206.8g

20. A silver spoon is being used to stir a very hot meal. If the temperature is increased from 20ºC to

49ºC and 400J of energy was used what is the mass of the spoon? 60g