An astronaut in space needs to absorb 2,400KJ of solar energy in a container with an accurately known volume of water. The water's temperature is needed to increase from 20°C to 34.5°C. What amount of water is in the container?
The energy absorbed
by the water is given by the expression below
Energy = heat capacity X temperature
rise X mass of water
2,400,000 = 4.18J/g/°C
X 14.5°C X mass of water
39.6Kg = mass of water
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1 a) 80ml of water form 17°C to 50°C;
Temperature rise
= 50°C - 17°C = 33°C
mass = 80 grams
Specific heat = 4.18 J /g/°C
Energy required = 4.18 J /g/°C X 80g X 33°C = 11.035KJ
b) 2.3 litres of water from 34°C to 100°C;
Temperature rise
= 100°C
- 34°C = 66°C
mass = 2,300 grams
Specific heat = 4.18 J /g/°C
Energy required = 4.18 J /g/°C X 2300g X 66°C = 634.524KJ
c) 200g of cooking oil from 23°C to 100°C
Temperature rise = 100°C
- 23°C = 77°C
mass = 200 grams
Specific heat = 2.2J /g/°C
Energy required = 2.2 J /g/°C X 200g X 77°C = 33.88KJ
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3,450,560J
of energy are absorbed by 300kg of water. If the initial temperature of the
water is 20°C what is
the final temperature?
The energy absorbed
by the water is given by the expression below
Energy = heat capacity X temperature
rise X mass of water
3.450,560 = 4.18J/g/°C
X °C X 300,000
3,450.560/4.18/300,00 = change in
temperature =2.75
Final temperature is 20°C + 2.75°C = 22.75°C
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A peanut of mass 2.34g is burnt in a calorimeter containing 100ml of water. If the temperature of the calorimeter rises from 23.5°C to 27.7°C calculate the energy content of the peanut in joules per gram.
The energy absorbed
by the water is given by the expression below
Energy = heat capacity X temperature
rise X mass of water
Energy = 4.18J/g/°C X
4.2°C X 100g
Energy =1.76KJ
Energy/gram = 1.76/2.34
=750.2Joules/gram
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When 0.15 gram of heptane was burnt in a bomb calorimeter containing 1.5kg of water the temperature rose from 22.000°C to 23.155°C. Calculate the heat given out by heptane during combustion per mole. This is known as the heat of combustion.
Energy = heat capacity
X temperature rise X mass of water
7.242KJ = 4.18J/g/°C
X 1.155°C X 1,500
Mole of heptane = 0.15 / 102 = 0.0015
Energy/mole= 4,827.9KJ/mole
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Specific heat capacity |
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Have you noticed how some substances can absorb a great deal more energy than others before increasing their temperature? Out in the hot summer sun a bucket of sand will get hotter than a bucket of water even though they both have absorbed the same amount of solar energy. A pot of oil will get hotter quicker over the stove than the same amount of water placed in the same pot. Why? Substances absorb thermal energy in their bonds. When certain materials absorb energy their increase in temperature depends on their ability to store thermal energy in their bonds. The amount of energy required to raise the temperature of 1 gram of substance by 1 degree Celsius is known as the specific heat capacity of that substance. Water has one of the highest heat capacities with a value of 4.18J/g/°C. Cooking oil has a heat capacity of 2.2J/g/C while sand has a value of 0.48J/g/°C. The hydrogen bonding between water molecules gives the liquid a high specific heat capacity. How do we use
specific heat in our calculations? |
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1) Calculate the energy required to boil 100ml of water for a cup of tea if the initial water temperature is 27.0°C. (The density of water is 1g/ml) Since the density of water is 0.997g/ml , at 25oC we can round it to 1.00 g/mL. So 100ml of water has a mass of 100 grams. The change in temperature is (100°C - 27°C) = 73°C. Since the specific heat of water is 4.18J/g/°C we can calculate the amount of energy needed by the expression below. Energy required = 4.18 J/g/°C X 100g X 73°C = 30.514KJ. Try some exercises. An
astronaut in space needs to absorb 2,400KJ of solar energy in a container
with an accurately known volume of water. The water's temperature is
needed to increase from 20°C
to 34.5°C. What amount
of water is in the container? 3,450,560J
of energy are absorbed by 300kg of water. If the initial temperature
of the water is 20°C
what is the final temperature? A
peanut of mass 2.34g is burnt in a calorimeter containing 100ml of water.
If the temperature of the calorimeter rises from 23.5°C
to 27.7°C calculate the energy content of the peanut in joules per
gram. When 0.15 gram
of heptane C7H16 was burnt
in a bomb calorimeter containing 1.5kg of water the temperature rose
from 22.000°C to 23.155°C. Calculate the heat given out by heptane
during combustion per mole. This is known as the heat of combustion. |
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Continue
with some more exercises involving specific heat capacity.
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