Measuring Heat
Definitions:
Joule (J) - named after James Joule. Labeled in an equation as "q", a unit of energy. It requires 4.184 J to
raise the temperature of 1 gram of water by 1 oC.
Watt (W) - after James Watt. A derived unit: 1 Watt = 1 J/second
Sample Problem #1 An electric kettle delivers 144,00 J of energy to the water in it in 2 minutes.
What is the power of the kettle?
P = Q/t = 144,000 J / 2 min * 60 sec/ min = 144,000 J / 120 sec = 1200 J/s = 1200 W
Sample Problem #2 A 100 watt immersion heater used in a tropical fish tank is used to heat the water in
a beaker for 3 minutes. How much energy was transferred to the water?
P = Q/t therefore Q = P * t = 100 W * 3 min = 100 W * 180 sec = 18,000 J = 18 kJ
The Capacity to Hold Heat
When heat is added to a substance it's temperature increases. There is a direct relationship between the
temperature reached and the heat added.
There is another direct relationship between the mass of a substance and the heat needed to make the
substance undergo a given change in temperature.
Water is the principle substance used because it was water that was used to define the energy unit and
water is readily accessible and relatively safe to use.
Imperial Heat Unit
The calorie (cal) was defined to be the amount of heat required to raise 1 gram of water by 1 degree
Celsius.
If you had 100 grams of water it would take 100 calories of heat energy to raise it's temperature by 1 oC.
This is became a definition and was called the Specific Heat Capacity. The symbol used in equations to
describe the Specific Heat Capacity is 'c' and the units are J/g oC
For example the Specific Heat Capacity of water is 1 cal/g oC = 4.184 J/goC (Metric definition)
Heat Capacity is either the amount of heat required to increase the temperature of a substance by 1.0 oC or
the amount of heat released to the environment to cool a substance by 1.0 oC
Specific Heat Capacity Table
Substance
Specific Heat Capacity
at 25oC in J/goC
H2 gas
14.267
He gas
5.300
H2O(l)
4.184
lithium
3.56
ethyl alcohol
2.460
ethylene glycol
2.200
o
ice @ 0 C
2.010
o
steam @ 100 C
2.010
vegetable oil
2.000
sodium
1.23
air
1.020
magnesium
1.020
aluminum
0.900
Concrete
0.880
glass
0.840
potassium
0.75
sulphur
0.73
calcium
0.650
iron
0.444
nickel
0.440
zinc
0.39
copper
0.385
brass
0.380
sand
0.290
silver
0.240
tin
0.21
lead
0.160
mercury
0.14
gold
0.129
To calculate the Specific Heat Capacity you need the following equation: Q = mc ΔT
c = Q / m ΔT
where c is the specific heat capacity
Q is the energy
m is the mass of the substance
ΔT is the temperature change
Sample Problem #3
An immersion heater issued to warm 500 grams of a liquid from 35oC to 55oC. If 20 kJ of energy are
given to the liquid, determine the specific heat capacity and use it to suggest an identity for the liquid.
c = Q/m ΔT = 20 kJ / 500 g * (55oC - 35oC) = 20,000 J / 500 g * 20oC = 2.00 J/goC
Based on the calculated value of 'c' the substance may be vegetable oil.
Principle of Heat Transfer
This comes from an understanding of the Law of Conservation of Mass and Energy. You know that
hotter objects transfer heat energy to colder objects. Hotter objects get colder, colder objects get
hotter.
QHeat Released by the Hot Object = QHeat Gained by the Cold Object
since Q = mc ΔT
then
mhch ΔTh = mccc ΔTc
And if both substances are the same then ch = cc can be eliminated. (where ch is the specific heat
capacity of the hot substance and cc is the specific heat capacity of the cold object.)
mh ΔTh = mc ΔTc
Sample Problem #4
If 80 grams of water at 70oC is mixed with a caertain mass of cool water at 20oC, the final temperature of
the mixture is 60oC. What is the mass of the cool water.
Q h = Qc
mhch ΔTh = mccc ΔTc
since we are using water for both the hot and cold sides of the equation we can cancel out the c h = cc
therefore
mh ΔTh = mcΔTc
mc = mh ΔTh = 80 g X (Ti - Tf)
Δ Tc
(Tf - Ti)
= 80 grams X (70oC - 60oC) = 80 g X 10oC = 20 grams
(60oC - 20oC)
40oC
The initial mass of the cold water used was 20 grams.
Sample Problem #5
If 400 grams of water at 60oC are mixed with 100 grams of water at 10oC, what is the final temperature of
the mixture?
Qh = Qc
mh ΔTh = mcΔTc
400 g X (60oC - Tf) = 100 g X (Tf - 10oC)
24000 - 400Tf oC = 100Tf oC - 1000
25000 = 500Tf oC
Tf = 25000/500 oC = 50oC
Sample Problem #6
A piece of metal with a mass of 500 grams and unknown specific heat capacity is placed in boiling water
at 100oC. The hot metal is then transferred quickly into a 200 grams sample of water at 20 oC. If the final
temperature of the water-metal mixture is 30oC what is the specific heat capacity of the metal and
identify the possible identity of the metal.
Qh = Qc
mhch ΔTh = mccc ΔTc
ch = mccc ΔTc = 200 g X 4.184 J/goC X 10oC = 0.239 J/goC
mh ΔTh
500 g X 70oC
The metal is probably silver.
Specific Heat Questions
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Which kind of substance needs more energy to undergo a rise of 5 degrees in temperature something with a high specific heat or something with a low specific heat? Explain.
How much heat in kilojoules has to be removed from 225 g of water to lower its temperature from
25oC to 10.0oC? (This would be like cooling a glass of lemonade.)
To bring 1.0 kg of water from 25 oC to 99 oC takes how much heat input, in joules? In kilojoules? This
would be like making four cups of coffee.
Fat tissue is 85% fat and 15% water. The complete breakdown of the fat itself converts it to CO 2 and
H2O, and releases about 37.665 kJ/g (of fat in the fat tissue).
(a) How many kilojoules are released by a loss of 0.45 kg (1 lb.) of fat tissue in a weight-reduction
program?
(b) A person running at 13 km/hr expends about 2.0 X 103 kJ/hr of extra energy. How far does a
person have to run to "burn off" 0.45 kg of fat tissue by this means alone.
If a gold ring with a mass of 5.5 grams changes temperature from 25.0oC to 28.0oC, how much energy
(in joules) has it absorbed?
The specific heat of helium is 5.188 J/goC and of nitrogen is 1.042 J/goC. How many joules can one
mole of each gas absorb when its temperature increases 1.00oC?
We wish to determine how much heat paraffin gives off on burning. We use a candle flame to heat
some water in a calorimeter. These data were obtained:
Mass of water in calorimeter 350 g
Initial mass of candle 150 g
Final mass of candle 112 g
Initial temperature of water 15oC
Final temperature of water 23oC
Calculate:
a) the temperature rise,
b) the joules absorbed by the water in the calorimeter,
c) the grams of paraffin burned,
d) the approximate value of heat of combustion of paraffin in J/g.
Neglect the energy absorbed by the calorimeter.
Ethanol has a heat capacity of 2.51 J/goC. 25.00 grams of this at 40oC has been used to heat 500 mL
of water. What would have been the temperature change of the water if the alcohol ends up at 10 oC?
Ethyl alcohol in a container is lit. The heat produced during burning was used to heat a flask of
water. The data collected are shown below:
Mass of container plus ethanol, before burning 42.70 g
Mass of container plus ethanol, after burning 40.70 g
Mass of flask plus water 582.0 g
Mass of the empty flask 182.0 g
Initial temperature of the water 5.3oC
Final temperature of the water 35.3oC
Calculate the heat of combustion of ethyl alcohol.
100 grams of ethanol at 25oC is heated until it reaches 50oC. How much heat does the ethanol gain?
A beaker contains 50 grams of liquid at room temperature. The beaker is heated until the liquid gains
10oC. A second beaker contains 100 grams of the same liquid at room temperature. This beaker is
also heated until the liquid gains 10oC. In which beaker does the liquid gains the most thermal
energy? Explain
You know that ΔT = Tf - Ti. Combine this equation with the heat equation Q = mc ΔT to solve for the
following quantities.
a) Ti in terms of Q, m, c and Tf
b) Tf in terms of Q, m, C and Ti
How much heat is required to raise the temperature of 789 grams of liquid ammonia from 25.0oC to
82.7oC?
A solid substance has a mass of 250.00 grams. It is cooled by 25.00oC and loses 4937.50 J of heat.
What is it's specific heat capacity. Identify this substance.
A piece of metal with a mass of 14.9 grams is heated to 98.0oC. When the metal is placed in 75.0
grams of water at 20.0oC. The temperature of the water rises by 28.5oC. What is the specific heat
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capacity of the metal?
A piece of gold ( c = 0.129 J/goC) with a mass of 45.5 grams and a temperature of 80.5oC is dropped
into 192 grams of water at 15.0oC. What is the final temperature of the system?
When iron nails are hammered into wood, friction causes the nails to heat up.
a) Calculate the heat that is gained by a 5.2 gram nail as it changes from 22.0oC to 38.5oC?
b) Calculate the heat that is gained by a 10.4 gram nail as it changes from 22.0oC to 38.5oC?
c) Calculate the heat that is gained by a 5.2 gram nail as it changes from 22.0oC to 55.0oC?
A 23.9 grams silver spoon is put in a cup of hot chocolate. It takes 0.343 kJ of energy to change the
temperature of the spoon from 24.5oC to 85.0oC. What is the specific heat capacity of the silver?
The specific heat capacity of aluminum is 0.920 J/goC. The specific heat capacity of copper is 0.389
J/goC. The same amount od heat is applied to equal masses of these 2 metals. Which metal
increases more in temperature? Explain.
Explain why there is an energy difference between the following reactions.
CH4(g) + 2 O2(g) -----> CO2(g) + H2O(g) + 802 kJ
CH4(g) + 2 O2(g) -----> CO2(g) + H2O(l) + 890 kJ