1. Make the following conversions: a. 0 ºC to kelvins ( K) c. 273 ºC to kelvins ( K)
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1 Chapter 4 Heat Practice Problems (answers are in brackets) Name: Temperature Conversions: C = ( F 32) 5 9 F = ( 9 ) C K = C Make the following conversions: a. 0 ºC to kelvins ( K) c. 273 ºC to kelvins ( K) b. 0 K to degrees Celsius ( ºC) d K to degrees Celsius (0 ºC) 2. Convert these Celsius temperatures to Kelvin temperatures. a. 27 ºC (300 K) c ºC (89 K) b. 560 ºC (833 K) d ºC (impossible why?) 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 ( ºF) Thermal Linear Expansion: L = α L T 1. A 1.00 x 10 4 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)
2 4. By how much would you need to heat a 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 C. The length of the heated bar is measured to be exactly 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 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 10 6 J)
3 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 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 10 4 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 10 2 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 Aluminum Brass Carbon Copper Glass Ice Iron Lead Methanol Silver Steam Water Zinc Specific heat J/(kg ºC)
4 Transfer of Heat Energy: T f = m ac a T a,i + m b C b T b,i m a C a + m b C b 1. A 2.00 x 10 2 g sample of water at 80.0 ºC is mixed with 2.00 x 10 2 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 10 2 g sample of methanol at 16.0 ºC is mixed with 4.00 x 10 2 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 10 2 brass block at 90.0 ºC is placed in a Styrofoam cup containing 2.00 x 10 2 g of water at 20.0 ºC. No heat is lost. Find the final temperature of the mixture. (23.0 ºC)
5 4. A 1.0 x 10 2 g aluminum block at ºC is placed in 1.00 x 10 2 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 10 2 g mass of tungsten at ºC is placed in 2.00 x 10 2 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 10 2 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 ºC, determine the original temperature of the piece of zinc. (114 ºC)
6 Specific Latent Heat of Fusion and Vapourization: Q = m H f and Q = m H v and Q = mc T 1. How much heat is absorbed by 1.00 x 10 2 g of ice at ºC to become water at 0.0 ºC? ( J) 2. A 2.00 x 10 2 g sample of water at 60.0 ºC is heated to steam at ºC. How much heat is transferred? (5.02 x 10 5 J) 3. How much heat is needed to change 3.00 x 10 2 g of ice at -30.0ºC to steam at 130.0ºC? (9.40 x 10 5 J)
7 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? ( J) 5. How much heat is required (transferred) to change 10.0 g of steam at ºC to ice at ºC? ( J) Material Heats of Fusion and Vaporization of Common Substances Heat of fusion H f (J/kg) Heat of vaporization H v (J/kg) Copper Gold Iron Lead Mercury Methanol Silver Water (ice) 2.05 x x x x x x x x x x x x x x x x 10 6
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