Pre-Lab - The Mechanical Equivalent of Heat
The units for energy are numerous and can be confusing. Physics texts have solved that
problem by using only the standard units for energy. That is, Joules are the SI unit of
energy , but there are also other units in use. In the “real world” there are many energy
units. There are units for thermal energy such as calories (1 calorie = 4.186 J) and BTU’s
(1 BTU = 252 calories). Electrical energy is sold to you kWh (1 kWh = 3.61 x 106 J).
Natural gas is sold in therms (1 therm =105 BTU). Electron volts (eV = 1.6 x 10-19 J) are
used on the atomic scale. There is even an energy unit that is called a quad (1 quad =
1015 BTU) that is used to measure the energy consumption of the United States. The
energy consumption of the United States was 98 quads in 2003. The energy content of
food is measured in Calories (1 Calorie = 1000 calories = 1 kilocalorie).
Questions
1.
If a person’s food energy intake is 2400 kilocalories per day and if all this
energy eventually is given off as heat, what is the average rate of heat output of
a person in watts?
2.
In the northern hemisphere, the average power hitting the surface of the earth
700 W/m2. Plants can convert about 10% of the solar energy into plant cells
and cows that eat the plants convert about 10% of that plant energy into meat.
If humans need 2400 kilocalories per day of meat energy and we assume that
they eat only meat, how many square meters of space is needed to support one
human.
3.
The United States has 9.16 x 106 km2 of dry land. The amount of land that is
put into crops is 21 % of the total land. Using the results of question 2 above,
what is the size of the population that the land of the U.S. could support?
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Laboratory: The Mechanical Equivalent of Heat
Theory:
The mechanical equivalent of heat is the relationship between units of heat energy and
units of mechanical energy. Heat energy has traditionally been measured in units of
calories and likewise mechanical energy is measured in Joules. However, since heat is a
form of energy, it also could be measured in Joules. The SI unit for energy has been
designated as Joules.
The unit of calorie is defined at the heat energy needed to raise 1 gram of water one
degree Celsius. Therefore, the heat capacity of water is C = l calorie/g/°C. In general,
the heat absorbed by a body is given by
Q = m C DT
(1)
where Q is the heat gained in calories, m is the mass, DT is the temperature change, and
C is the heat capacity of the body.
In this experiment, frictional forces heat an aluminum calorimeter. The work of friction
should be equal to the heat energy gained by the calorimeter. The heat energy gain can
be easily found by measuring the change in temperature (DT) and by knowing the mass
of the aluminum calorimeter (Mc).
The heat energy gain Q is given by Equation (2).
Q = Mc Cc DT
(2)
where Cc = 0.220 cal/(g °C)
A nylon cord is wound five times around the aluminum calorimeter. The frictional force
between the band and the calorimeter is large enough that one end of the band can lift a 5
kg weight while the other end becomes slack. As a result of this mechanical trick, the
frictional force is equal to the weight of the 5 kg mass and is to a large extent independent
of the speed at which the drum is rotated. The work of friction (Wf ) is
Wf = Ff • S = M g C n
(3)
where C is the circumference of the aluminum drum, n is the number of turns, and M is
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the mass of the suspended weight.
Procedure:
1.
Measure the mass of the calorimeter.
2.
Measure the mass of the hanging weight.
3.
Measure the diameter of the calorimeter drum using a vernier caliper and calculate
the circumference from the equation, c = π d
4.
Record the initial temperature. This can be found by measuring the resistance of the
thermistor that has been embedded in the calorimeter and using the supplied
conversion table.
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5.
Secure the calorimeter and wind the
nylon cord round it five times. One end
of the cord is drawn through the loop.
The other end is hooked to the weight
by a cord.
6.
Read the temperature and then turn the
handle for your number of rotations.
Record the final temperature.
Data:
Mass of Calorimeter = ______________
Mass of the hanging weight = ___________
Thermistor resistance at the initial temperature = __________ W = ________oC
Thermistor resistance at the final temperature = ___________ W = _______oC
Number of turns = ______________
Circumference of the drum = ________________
Evaluation of the measurement
1.
Calculate the heat absorbed using (Equation 2).
2.
Calculate the work done by friction using (Equation 3).
3.
Calculate the number of Joules in a calorie. The accepted value is 4.186 Joules
= 1 calorie. Find your percent error.
Revised 8/25/16
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