Name: _______________________________
Chapter 4 – Heat
Practice Problems (answers are in brackets)
Temperature Conversions:
𝟓
°𝑪 = (°𝑭 − 𝟑𝟐) × 𝟗
𝟗
°𝑭 = (𝟓) °𝑪 + 𝟑𝟐
1. Make the following conversions:
a. 0 ºC to kelvins (273.15 K)
𝑲 = °𝑪 + 𝟐𝟕𝟑.15
c. 273 ºC to kelvins (546.15 K)
b. 0 K to degrees Celsius (-273.15 ºC)
d. 273.15 K to degrees Celsius (0 ºC)
2. Convert these Celsius temperatures to Kelvin temperatures.
a. 27 ºC (300 K)
c. -184 ºC (89 K)
d. -300 ºC (impossible – why?)
b. 560 ºC (833 K)
3. Convert the following:
a. 150 ºF to ºC (66 ºC)
c. 323 K to ºC (49.9 ºC)
b. 37 ºC to ºF (99 ºF)
d. 147 K to ºF (-195.1 ºF)
Thermal Linear Expansion:
∆𝐿 = 𝛼 ∙ 𝐿 ∙ ∆𝑇
4
1. A 1.00 x 10 metre steel railroad track with a coefficient of linear expansion of 12 x 10-6 °C-1 changes
temperature from 18°C to 38°C. By how many metres will the railroad tracks expand? (2.4 m)
2. Railroad tracks are segmented into short pieces. Why is this a good idea in a place like
Saskatchewan?
3. The Eiffel Tower in Paris is 324 metres tall and is made primarily of iron, which has a coefficient of
linear expansion of 12 x 10-6 °C-1. The average low in Paris is 1.00°C and the average high is
24°C. What is average change in height the tower experiences each year? (0.089 m)
4. By how much would you need to heat a 120.0 inch bar of zinc to make it expand by one inch? The
coefficient of linear expansion of zinc is 30 x 10-6 °C-1. (280 °C)
5. A metal bar changes in length by 1.00 metre with a 150 °C change in temperature. Its coefficient of
linear expansion is 25 x 10-6 °C-1. What is the metal bar’s original length? (270 m)
6. An unknown metal alloy is being tested to discover its thermal properties to see if it is suitable for use
as a component in an aircraft wing. The alloy is formed into a bar measuring 1.00 metre in length, and
is then heated from its starting temperature of 30 °C to a final temperature of 100.0 °C. The length of
the heated bar is measured to be exactly 1.002 metres in length. What is the coefficient of thermal
expansion of the alloy to 2 significant figures? (2.9 x 10-5 °C-1)
7. The aircraft wing from #6 experiences temperature extremes that span 210°C. The component for the
wing will have a length of 3.00 meters. Testing indicates that the aircraft wing will remain stable
only if the component never expands to a length larger than 3.017 meters. If the component is made
from the metal alloy in question, will it meet this requirement? (No)
8. A rod 1.0 m long expands 0.50 mm when heated from 20.0 °C to 84.0 °C. What is the coefficient of
linear expansion of the material from which the rod is made? (7.8 x 10-6 °C-1)
Specific Heat Capacity – see table of specific heat on the back page.
𝑄 = 𝑚𝐶∆𝑇
1. How much heat is absorbed by 60.0 g of copper when it is heated from 20.0 ºC to 80.0 ºC? (1390 J)
2. A 38 kg block of lead is heated from -26 ºC to 180 ºC. How much heat does it absorb during the
heating? (1.0 x 106 J)
3. The cooling system of a car engine contains 20.0 L of water. (1 L of water has a mass of 1 kg). What
is the change in the temperature of the water if the engine operates until 836.0 kJ of heat are added?
(10.0 ºC)
4. A 565 g cube of iron is cooled from the temperature of boiling water to room temperature (20 ºC).
a. How much heat must be absorbed from the cube? (2.0 x 104 J)
b. If the iron is cooled by dunking it into water at 0 ºC that rises in temperature to 20 ºC, how
much water is needed? (0.24 kg)
5. How much heat is needed to raise the temperature of 50.0 g of water from 4.5ºC to 83.0 ºC? (16000 J)
6. A 5.00 x 102 g block of metal absorbs 1880 J of heat when its temperature changes from 20.0 ºC to
30.0 ºC. Calculate the specific heat of the metal. Identify the metal. (376 J/(kgºC) - brass)
7. A copper wire has a mass of 165 g. An electric current runs through the wire for a short time and its
temperature rises from 21 ºC to 39 ºC. What minimum quantity of energy is converted by the electric
current? (1100 J)
Specific Heat of Common Substances
Material
Specific heat J/(kg • ºC)
Aluminum
903
Brass
376
Carbon
710
Copper
385
Glass
664
Ice
2060
Iron
450
Lead
130
Methanol
2450
Silver
235
Steam
2020
Water
4180
Zinc
388
Transfer of Heat Energy:
𝑻𝒇 =
𝒎𝒂 𝑪𝒂 𝑻𝒂,𝒊 + 𝒎𝒃 𝑪𝒃 𝑻𝒃,𝒊
𝒎𝒂 𝑪𝒂 + 𝒎𝒃 𝑪𝒃
1. A 2.00 x 102 g sample of water at 80.0 ºC is mixed with 2.00 x 102 g of water at 10.0 ºC. Assume no
heat loss to the surroundings. What is the final temperature of the mixture? (45.0 ºC)
2. A 4.00 x 102 g sample of methanol at 16.0 ºC is mixed with 4.00 x 102 g of water at 85.0 ºC. Assume
no heat loss to the surroundings. What is the final temperature of the mixture? (59.5 ºC)
3. A 1.00 x 102 brass block at 90.0 ºC is placed in a Styrofoam cup containing 2.00 x 102 g of water at
20.0 ºC. No heat is lost. Find the final temperature of the mixture. (23.0 ºC)
4. A 1.0 x 102 g aluminum block at 100.0 ºC is placed in 1.00 x 102 g of water at 10.0 ºC. The final
temperature of the mixture is 25 ºC. What is the specific heat of the aluminum? (840 J/(kgºC))
5. A 1.00 x 102 g mass of tungsten at 100.0 ºC is placed in 2.00 x 102 g of water at 20.0 ºC. The mixture
reaches equilibrium at 21.6 ºC. Calculate the specific heat of tungsten. (171 J/(kgºC))
6. A 5.00 x 102 g sample of water is at 15.0 ºC. A 40.0 g block of zinc is placed in the water. If the final
temperature of the water is 15.73 ºC, determine the original temperature of the piece of zinc. (114 ºC)
Specific Latent Heat of Fusion and Vapourization:
𝑸 = 𝒎 ∙ 𝑯𝒇
and
𝑸 = 𝒎 ∙ 𝑯𝒗 and
𝑸 = 𝒎𝑪∆𝑻
1. How much heat is absorbed by 1.00 x 102 g of ice at -20.0 ºC to become water at 0.0 ºC? (3750000 J)
2. A 2.00 x 102 g sample of water at 60.0 ºC is heated to steam at 140.0 ºC. How much heat is
transferred? (5.02 x 105 J)
3. How much heat is needed to change 3.00 x 102 g of ice at -30.0ºC to steam at 130.0ºC? (9.40 x 105 J)
4. Years ago, a block of ice with a mass of about 20.0 kg was used daily in a home icebox. The
temperature of the ice was 0.0 ºC when delivered. As it melted, how much heat did a block of ice that
size absorb? (6680000 J)
5. How much heat is required (transferred) to change 10.0 g of steam at 120.0 ºC to ice at -20.0 ºC?
(-30900 J)
Material
Copper
Gold
Iron
Lead
Mercury
Methanol
Silver
Water (ice)
Heats of Fusion and Vaporization of Common Substances
Heat of fusion Hf (J/kg)
Heat of vaporization Hv (J/kg)
2.05 x 105
6.30 x 104
2.66 x 105
2.04 x 104
1.15 x 104
1.09 x 105
1.04 x 104
3.34 x 105
5.07 x 106
1.64 x 106
6.29 x 106
8.64 x 105
2.72 x 105
8.78 x 105
2.36 x 106
2.26 x 106