National Taiwan Normal University General Physics Experiment Handout Editing Group
12. Experiment: measurement of specific heat
Purpose:
Determine the specific heat of aluminum blocks at the temperature between 45℃ and
65℃ using the heat transfer phenomenon.
Instrument:
Equipment
quantity Equipment
quantity
Plastic cup with lid
1
Electric kettle
1 set
Digital thermometers (available
2
Iron clip
1
Aluminum blocks
1
Pipette
1
stopwatch
1
Tape (shared)
Water (specific heat at 45℃
range -10℃~ 200℃)
Electronic scales (shared)
~65℃ is 𝟒. 𝟏𝟖𝟔
𝐉
𝐠℃
)
Preview steps:
Procedues:
Preview
1. Before the experiment, Familiarizewith
the principles and answer the questions
in the appendix.
2. Measure the mass of the aluminum block and record it.
3. Boiled hot water:
Place the electric kettle in the center of the experimental table and arrange the
wires to keep the device safe; Fill the kettle with water more than the edge of the
metal pan and put on the lid; Insert a thermometer in the middle of the lid and
adjust the heat setting to medium, as shown in Figure 1. Around 5 minutes, if the
thermometer shows that the temperature is higher than 80℃, reduce the heat to
low (hot water above 50℃ will cause burns, be careful when handling it.)
4. Place the aluminum block in the plastic cupand add cold water until the
aluminum block is completely covered.Mark the height of the water surface H
in the plastic cup with a small piece of tape, and empty the cup.
5. Turn on the digital thermometer to record room temperature Tr every 30
seconds, 5 times in total.
6. Add hot water into the plastic cup (at least 70℃). The amount of hot water
needs to reach the height H indicated in step 4. Put in a digital thermometer and
close the lid tightenly.
7. After the temperature of the water drops to 65℃, record the time t it takes for
the temperature decrease by 1℃. Plot the temperature-time curve of the system
from 65℃ to 45℃. Record the mass of the water m1.
8. Warm up aluminum block:
Put the aluminum block into the plastic cup and fill with hot water (at least 70
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National Taiwan Normal University General Physics Experiment Handout Editing Group
℃) to warm up the aluminum block. When the aluminum block reaches 70 ℃,
use the iron clip to hold the aluminum block and remove the water from the cup.
Repeat the step if needed.
9. Add hot water (at least 70℃) to the plastic cup until the water level reaches the
same height H; Put in a digital thermometer and close the lid tightly.
10.When the temperature of the water drops to 65℃, record the time t it takes for
the temperature to drop by 1oC. Plot the temperature-time curve of the system
from 65℃to 45℃. Record the mass of the hot water m2 and the aluminum block
m.
11.After the experiment is completed, repeat step 5 and measure the room
temperature 5 times. Calculate the average Tr and the standard deviation △Tr
with the room temperature data before the experiment.
12.Using the experimental data and the formulas from Appendix, Question 1, and
Question 3, to determine the K value, and its uncertainty △K. Calculate sAl and
kJ
)
kg  K
its uncertainty △sAl. (The specific heat of water is
Appendix - Principle:
In steps 2 and 3, the temperature drop in the plastic cup is caused by heat exchange
between the substance in the cup (ignoring the thermal capacity of the plastic cup at this
stage) and the surrounding environment. According to Newton's law of cooling, the heat
exchange is proportional to the temperature difference between the two, i.e.
(1)
−CdT =  (T − Tr )dt
where C is the thermal capacity (C1 or C2) and α is a proportional constant. The integral
of (1) is

− t
T − Tr = (T0 − Tr )e C
(2)
where T0 is the initial temperature of the water in the cup. Take the log of (2), which
makes it linear. Thus, obtain
𝛼
log(𝑇 − 𝑇𝑟 ) = log(𝑇0 − 𝑇𝑟 ) − ( log 𝑒)𝑡
(3)
𝐶
From this relationship above to find the value of K and its uncertainty △K, and
determine the value of sAl, and estimate its uncertainty △sAl.
Calculate the specific heat of the aluminum block from 45oC to 65oC.
Questions:
1. Derive the mathematical formula of the specific heat of aluminum sAl using the
measurable physical quantities: hot water mass m1 in step6, hot water mass m2
in step 10, aluminum block mass m, water specific heat cw, and the ratio of
thermal capacity K=C1/C2. (C1 is the thermal capacity of water in step 6, C2 is
the thermal capacity of water and aluminum blocks mixture in step 10, and C1,
C2 are not included in the formula of aluminum specific heat.)
2. From (3), plot two curves of log(𝑇1 − 𝑇𝑟 ) vs time and log(𝑇2 − 𝑇𝑟 ) vs time.
What is the physical meanings of the slope and the intercept of these two trend
lines? And illustrate the way to find the value of K and its uncertainty △K from
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these two trend lines.
thermometer
metal pan
Power Knob
Figure 1
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