4. Heat and Thermal Energy
Introduction
The purpose of this experiment is to study cooling and heating by conduction, convection, and
radiation.
Thermal energy is the energy of random molecular motion. Heat is thermal energy transferred. If
heat Q is added or removed from an object, then the temperature of the object changes. The heat
added or removed Q and the change in temperature ΔT are related by:
Q = mcΔT
(J)
(1)
where m and c are the mass and specific heat of the substance. Heat Q is transferred by
conduction, convection, or radiation.
The rate of transferring energy by conduction is given by:
P=
Q
ΔT
= kA
Δt
L
(J/s) or (W)
(2)
where k, A, and L are the thermal conductivity, the cross-sectional area, and the length or
thickness. In the figure T > To.
L
T
A
T0
Q
The rate of transferring energy by radiation is given by:
P = σAe(T4 – Te4)
(W)
(3)
where σ is a constant, A is the surface area of the object, e is the emissivity of the surface
(o<e<1), T is the surface temperature of the object in kelvins, and Te is the temperature of the
enviroment.
There is no simple equation that describes heat transfer by convection.
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Objectives
•
•
•
•
To become familiar with the different mechanisms of heat transfer.
To verify the law of conservation of energy.
To learn to calculate and measure the amount of energy needed to raise the temperature of
different substances.
To review methods of graphically analyzing non-linear data sets.
Prelab Questions
1. How does heat transfer by conduction change if the thickness L is changed? In particular, if
the thickness of object is doubled, then the rate of heat transfer by conduction will
_________ by a factor of ____________.
2. How does the power radiated by an object change if the temperature T of the radiating object
changes? Here we ignore the surroundings at temperature Te. In particular, if T is halved,
then the power radiated ____________ by a factor of _________.
3. The star Betelguese has a radius and surface temperature of about 108 miles and 3000 K. The
sun has a radius and surface temperature of about 5 × 105 miles and 6000 K. The ratio of the
power radiated by the sun and Betelguese, PSun/ PBet, is ____________. Assume the
emissivity of the stars is the same. The surface area of a sphere is A = 4πr2.
Cooling by Conduction
In this part of the lab you will measure the temperature of a canister of water as it cools primarily
through conduction.
Computer setup
1. Connect the Data Studio interface to the computer, turn on the interface, and then turn on the
computer.
2. Double click on the Data Studio icon. When the window opens click on Create Experiment.
3. Plug the Temperature Sensor into Analog Channel A
4. In the Sensors panel on the left, scroll down to Temperature Sensor and double click. An
icon for the temperature sensor will appear in the right panel.
5. Create a Temperature graph.
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Data collection
1. The apparatus, shown below, is a nested set of canisters. Remove the inner canister and fill
the larger canister to the line marked inside with tap water. Insert the temperature sensor into
the lid such that the end of the sensor reaches about the middle of the smaller canister. Place
the smaller canister with its supporting ring inside the larger canister. It will float. Carefully
fill the smaller canister with boiling water and place the lid on the system.
2. To record the temperature, double click on Start. Stir continuously during the cooling
process. After about 400 s click on Stop. Print the graph for your notebook.
Stirrer
Temp sensor
Interface
Digital Analog
computer
Inner
canister
Question 1. From your graph, when the system was cooling did it cool faster at the beginning of
the experiment or toward the end of the experiment? Is this what you would expect from
equation (2)? Explain.
Heating
In this part of the experiment electrical energy is converted to thermal energy. You will measure
the energy dissipated by a metal coil in a canister of water and compare it to the change in the
water’s thermal energy. The apparatus you will use is shown below.
To Interface
Power
Supply
Temp
sensor
Stirrer
Heater
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Data Collection
1. Empty the water from both the outer and inner canisters. Weigh the inner canister, and then
add 200 ml of cold tap water to the small canister and again weigh the canister with the water
in it. Record the mass of the canister (mc) and the mass of water (mw) in kg.
2. Place the small canister inside the empty larger one. Position the end of the temperature
sensor in the middle of the small canister.
3. Set up the computer so that a Graph of temperature vs. time is on the screen, and set the
Maximum and Minimum times to 400 and 0 seconds. Double click on Digits in the lower
left corner of the screen to create a numerical readout of the temperature. Start recording
data, and record the initial temperature (Ti) in your notebook. Turn on the power supply and
set the voltage to 10.0 V.
4. Record the voltage (V) and current (I) from the power supply. Continue to stir the water
while the power supply is on.
5. After about 300 s turn off the power supply and click Stop. Measure Δt from your graph and
measure the final temperature (Tf) from the digital meter. Calculate the change in temperature
of the water ΔT = Tf – Ti.
Data Analysis
6. First skip ahead to the section “Cooling by Radiation and Convection” and start the
experiment. While the computer is collecting data you can analyse this data.
7. The electrical power is the current I in amperes (A) times the voltage in volts (V). The
electrical energy dissipated during time Δt is:
E = IVΔt
(Joules)
(4)
Calculate how much energy was produced by the power supply while you were heating the
water.
8. The heat input to the water during that time is:
Q = mw cw ΔT + mc cc ΔT
(Joules)
(5)
where the specific heats are cw = 4,186 J/kg•°C and cc = 900 J/kg•°C. This takes into account
the energy needed to heat the water plus the energy needed to heat the canister. With your
data calculate how much energy was used to heat the water and canister by ΔT.
Question 2. Was the heat Q transferred to the water greater or less than the energy E dissipated
by the resistive wire? Explain why you might expect there to be a discrepancy between these two
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values. Calculate the % discrepency between the heat input to the water and the electrical energy
dissipated.
Cooling by Radiation and Convection
Newton’s law of cooling states that the rate at which an object cools in proportional to the
difference between its temperature and the surrounding temperature. That is the temperature T
will decreases exponentially with time t:
T (t ) = (T0 − Te )e − ct + Te
(6)
where c is a constant with units of 1/sec, T0 is the objects initial temperature, and Te is the
temperature of the enviroment. In this part of the lab you will test to see if cooling by radiation
and convection obey Newton’s law of cooling.
1. Set up the computer so that a Graph of temperature vs. time is on the screen, and set the
Maximum and Minimum times to 20 and 0 minutes.
2. Carefully fill the black can about 2/3 full with hot water. Replace the lid and insert the
thermistor into the center of the can.
3. Wait 5 minutes for the temperature of the can and water to come to equilibrium. Then start
recording the temperature as a function of time.
4. Take data for at least 20 minutes and then click Stop. Print the graph for your notebook.
Question 3. Does Newton’s law of cooling appear to be satisfied?
4. Answering question 3 based on this graph alone can be challenging. A much better option
would be to create a semilog plot like we did in the last experiment. In order to do this export
your data as a text file (Display  Export Data), then open this file with excel. You should
have two collumns of data: time and temperature. Subtract room temperature (Te) from your
temperature data and take the natural log of this difference and plot this as a function of time.
Based on equation (6) what should your graph look like? Find the equation of the best-fit line
and again answer question 3. What is the constant c for your system? Print out this graph and
add it to your notenbook.
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