Questions of Transfer of Energy: Heat
A) Temperature and Scales
1. - Arrange the following temperature values from highest to lowest: 482 ° F, 102.1 ° C,
303.2 ° C; 319.16 K, 301.36 K, 233.6 ° F.
2. - In an American movie the main starring refers to the temperature of an ice block and
says its temperature is 14 º. Will there be an error in translation? What is the temperature
of the block? Sol: - 10ºC
3. - Convert the following values of temperatures in degrees Celsius: 86 º F, 122 º F, 158 º
F, 176 º F, 400 º F.
4. - Convert the following temperature values in degrees Fahrenheit: 65.5 ° C, 35 ° C,
168.5 ° C, -15 ° C, -120 ° C.
5. - Convert the following temperature values in degrees Kelvin: 87 º C, 129 º C, 358 º C,
427 º C, 222 º C.
B) Heat, Specific heat , Heat capacity, Latent heat
1. - The specific heat of mercury is 0.14 J / g · K. What is this information? What is the
specific heat of mercury expressed in cal / g · K? Sol: 3,349·10-2 cal / g·K
2. - a) How much heat (in calories) is needed to raise 20 grams of water from 5 ºC to 40
ºC? Sol: 700 cal
b) How much heat (in calories) is needed to raise 250 grams of water from 80 ºC to 87 ºC?
Sol: 1750 cal
c) How many calories are needed to raise 50 grams of iron from 55 ºC to 200 ºC? The
specific heat capacity of iron is 0.11 cal / g ºC. Sol: 797,5 cal
3. - a) How many grams of aluminum can be heated from 90 ºC to 120 ºC if 500 calories
are applied? The specific heat of aluminum is 0.21 cal / g ºC. Sol: 79,4 g
b) What is the specific heat capacity of a substance if 400 calories cause 25 grams of it to
go from 60 ºC to 190 ºC? Sol: 0,123 cal / g ºC
c) What is the final temperature if 500 calories are applied to 40 grams of copper at 20 ºC?
The specific heat capacity of copper is 0.092 cal / g ºC. Sol: 156 ºC
4. - a) What is the change in the temperature if 75 calories are applied to 10 grams of
water? Sol: 7,5 ºC
b) What was the initial temperature if 250 calories were applied to 100 grams of gold and
the final temperature of the gold was 175 ºC? The specific heat capacity of gold is 0.031
cal / g ºC. Sol: 94ºC
5. - A granite bench, which is in the park, has increased its temperature from 18 ° C to 45 °C
by the action of sunlight. According to the heat specific capacity of granite is 0.192 kcal / kg ·
K, and that the bench has a mass of 490 kg, calculate the quantity of absorbed heat in the
process. Sol: 1,062·104 kJ
Questions of Transfer of Energy: Heat
6. - According to the following specific heat capacities:
7. - The latent heat of fusion of lead is 23.2 kJ / kg. According to this data, how much
heat should we supply to melt 30 g of lead? How much lead could be melted providing 2
kJ?
8. - A 100 grams portion of ice at -10 °C is immersed in 500 g of water at 80 ° C. Calculate
the mixture's equilibrium temperature. Sol: 52,43ºC
Data: C (water) = 4180 J / kg ºC; C (ice) = 2100 J / kg ºC; Lf = 334000 J / kg.
9. - Calculate how much heat should be supplied to 2.5 kg of ice at 0 ° C to be heated to
50 ° C. Data: Lf = 3.33 × 105 J / kg. Sol: 1,35 106 J
10.- A calorimeter contains 1180 g of water at 25 ° C and 100 g of water vapour at 100 ° C.
Calculate the final temperature of the system. Data: Lv = 2.26 · 106 J / kg
11. - 45g of water at 4 ºC is added to 150g of water at 75 ºC. What is the mixture's
equilibrium temperature? Sol: 58,6 ºC
Questions of Transfer of Energy: Heat
12.- Calculate how much heat should be supplied to 100 g of ice at -10 ° C to be
transformed into water vapour at 130 ° C. Sol: 73900 cal
13. - Suppose a piece of iron with a mass of 21.5 g at a temperature of 100.0 ° C is
dropped into an insulated container of water. The mass of the water is 132.0 g and its
temperature before adding the iron is 20.0 ° C. What will be the end of the system
temperature? Specific heat of iron is 0.449 kJ / kg K.
14. - A 12.48 g sample of an unknown metal, heated to 99.0 °C was then plunged into 50.0
mL of 25.0 °C water. The temperature of the water rose to 28.1 °C. Assuming no loss of
energy to the surroundings:
a) How many joules of energy did the water absorb? Sol: 648,52 J
b) How many joules of energy did the metal lose? Sol: 648,52 J
c) What is the heat capacity of the metal? Sol: 9,147 J / ºC
d) What is the specific heat of metal? Sol: 0.733 J g-1 °C-1
15. - In preparing a cold drink with a final temperature of 0 ºC, Mary mixes 50 g of ice at
–10 ºC with some juice at +10 ºC. Suppose the specific heat of the juice is 4000 J/(kg ºC),
the specific heat of ice is 2000 J/(kg ºC) and the latent heat of fusion of water and the juice
are the same, equal to 3 x 105 J/kg. Answer the following questions based on the
information provided. You may assume that the cup Mary uses in making the drink
insulates well so there is no heat loss during the mixing, i.e., ΣQ = 0.
a) What mass of juice should Mary add to the ice so that no ice is transformed into
liquid water and no liquid juice is transformed into solid juice? Sol: 25 g
b) What mass of juice should Mary add to the ice so that all the ice is just melted? Sol: 400 g
C) Thermal expansion of solids
16. - On a fairly cool rainy day when the temperature is 20 ºC the length of a steel rail road
track is 20 m. What will be its length in a hot day when the temperature is 40ºC
Coefficient of Linear expansion of steel = 1,1 10-6 K-1. Sol: 20,0004 m
17. - The length of the side of a metal cube at 20ºC is 5 cm. Given that the linear
expansivity of the metal is 4 10-5 K-1, find the volume of the cube at 120 ºC.
Sol: 126,50 cm3
18. - The linear expansivity of brass is 210-5 K-1. If the volume of a piece of brass is 10 cm3
at 0 ºC, what will be its volume at 100 ºC? Sol: 10,05 cm3
19. - A blacksmith heated a metal whose cubic expansivity is 6,3 10-6 K-1 . Which is its area
expansivity? Sol: 4,2 10-6 K-1
20. - There is an aluminum ring, 0.07 m in diameter at 5 ºC. There is also an aluminum
shaft whose diameter is 0.07003 m in diameter at 5 ºC. What temperature should the shaft
be cooled such that the ring will fit over the shaft. Sol: - 12,86 ºC
Data: (linear expansivity of aluminium = 2.4 · 10-5 K-1)
Questions of Transfer of Energy: Heat
21. - A copper wire has a length of 15 m, when its emperature is 20º C. If an electric
current circulates through it then its temperature rises to 420 ° C. How much will be
extended? Data: linear expansivity of copper: = 17.10 -6 ºC-1. Sol: 102 mm
22. - Calculate the change in length of a brass wire (α = 2.10 -5 ºC-1) of 10 m when its
temperature changes from 20 ° C to 70 ° C. Sol: 1 cm
23. - There is a square aluminum plate of 20 cm square at 30 ° C. At what temperature its
surface will be 34 mm2 bigger? Data: (linear expansivity of aluminium = 2.4 · 10-5 K-1)
Sol: 47,7 ºC
24. - A solid brass sphere whose radius at 0 ° C is 5 cm; then it is heated to 150 ° C.
Calculate its increase in volume knowing that its linear expansivity is α = 1,9.10 -6 K-1.
Sol: 0, 44 cm3
25.- Calculate the volume of a cylindrical can of iron (α (Fe) = 1.2 · 10-5 K-1) at 100 ° C, if it
is 20 cm in diameter and 70 cm high, at 0 ° C. Sol: 22,07 dm3