DETERMINATION OF SPECIFIC HEAT CAPACITY OF AN UNKNOWN METAL
Background
When two substances at different temperatures are in contact, heat is transferred from the warmer substance to the cooler
substance. The heat lost, Qlost, by the warm substance is equal to the heat gained, Qgain, by the cooler substance, but ideally
the total heat of the system remains constant.
(1)
(2)
(3)
Qsystem = 0
Qlost + Qgain = 0
–Qlost = +Qgain
so
In this experiment, a warm metal object is placed in an aluminum calorimeter containing cooler water. The metal loses heat and
cools down while the water and inner cup of the calorimeter gain heat and its temperature increases. These changes in
temperature without a change of state are related to the heat change, ∆H, by
or Q = m c (T f – Ti)
Q = m c ∆T
(4)
where c is the specific heat capacity of the substance, Tf is the maximum final temperature of the system
(metal, water, and calorimeter), and Ti is the initial temperature of the substance. The maximum temperature is used because it
will be higher than room temperature, so the system (calorimeter and contents) will lose heat to the surroundings over time.
(5)
(6)
–Qmetal = +Qw+cal
–mm cm ∆Tm = (mw cw ∆Tw) +(mcal ccal ∆Tcal)
In this experiment the initial temperature of the water and calorimeter will be the same (thermal equilibrium) before the warm
unknown metal is added and each will have the same final temperature as the rest of the system, so the ∆T will be the same.
(7)
–mm cm ∆Tm = (mw cw + mcal ccal) ∆Tw+cal
Heat capacity, C, is the amount of heat energy required to change the temperature of an object by 1K (1 C°) and can be
calculated according to:
C=mc
(8)
mm cm ∆Tm = – (Cw + Ccal) ∆Tw+cal
mm cm ∆Tm = – (Cw+cal) ∆Tw+cal
Cw+cal = mw cw + mcal ccal
(9)
(10)
(11)
So equation 7, now becomes:
where
The specific heat capacity of water, cw, is known to be 4190 J kg –1K–1 and the specific heat capacity of the aluminum calorimeter
cup, ccal, is known to be 990 J kg –1K–1 (Tsokos, 2005, p177). The mass of the metal mm, the mass of the water mw, the mass of
the aluminum calorimeter cup, mcal, the temperatures of each just before combining them (Tim and Tiw+cal), and the maximum
temperature of the combination Tf will be measured. From these, the specific heat capacity of the metal cm can be determined.
cm =
-[mw ⋅ cw (T f − Tiw ) + mcal ⋅ ccal (T f − Tical )]
mm (T f − Tim )
or cm =
-C w + cal ∆Tw + cal )
mm ∆Tm
(12)
Materials
metal cylinder
beaker
tap water
graduated cylinder
Traditional Method
thermometer (± 0.5°C)
ScienceWorkshop/ DataStudio
temperature probe
Data Studio software
ScienceWorkshop interface
computer
Xplorer GLX
temperature probe
Xplorer GLX (hand-held data collection/processing)
aluminum calorimeter
electronic scale (±0.01 g)
hot plate or electric kettle
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Procedure
•
Find the mass of the metal cylinder and the small aluminum calorimeter cup using an electronic scale.
•
Put the metal in a hot water bath for 3 minutes until its temperature was the same as the water.
•
Find the temperature of the metal by taking the temperature of the hot water bath.
•
Use a graduated cylinder to measure enough tap water to completely cover the metal cylinder in the calorimeter
•
Put the measured volume of tap water in the calorimeter and find its constant temperature.
•
Keep the thermometer or temperature probe in the water while the metal is added.
•
Quickly and carefully transfer the metal from the hot water bath to the tap water in the calorimeter
•
Determine the highest temperature reached by the water and metal combination in the calorimeter
Using Data Studio and the temperature probe
Select DataStudio icon from the desktop
Connect the interface to the computer and plug into an outlet
Select Create Experiment
Click
(The computer should detect an interface)
and then select Temperature Sensor from the list of sensors
The data can be displayed as Graph or Digits
Graphs is easier to analyze later
To start data collection, press . ►Start
To stop data collection, press . ►Stop
.
.
To quickly get the initial and maximum temperatures, select Mean from the Show Selected Statistics button
Using Xplorer GLX
•
Turn on the Xplorer GLX with the temperature probe plugged in
•
The Temperature versus Time graph should appear
•
To start collecting data, press the big blue arrow ►
•
The temperature for the most recent reading are shown at the top of the window.
•
To stop collecting data, press the big blue arrow ►
•
Press the F1 (Auto Scale) button to enlarge the graph
•
The temperature values can be reviewed by pressing the < button to show coordinates along the plotted line
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Table 1.
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Constant values for all trials
Warm Metal Objects
mass of aluminum object, mAl / kg =
mass of unknown metal object, m m / kg =
initial temperature of metal, Tim / °C =
Table 2a
trial
Cooler Calorimeter and Water
mass of aluminum calorimeter cup, mcal / kg =
volume of water mass of aluminum cup, Vw / L =
initial temperature of water and calorimeter, Tiw+cal / °C =
Final temperatures for the aluminum object. * Initial temperatures of aluminum or water/calorimeter only included if they are not constant for all trials.
final temperature,
initial temperature of aluminum*
initial temperature of water and calorimeter*
T f / °C
T im / °C
Tiw+cal / °C
1
2
3
4
5
average
Table 2b
trial
Final temperatures for the unknown metal object. * Initial temperatures of unknown metal or water/calorimeter only included if they are not constant for all trials.
final temperature,
initial temperature of aluminum*
initial temperature of water and calorimeter*
T f / °C
T im / °C
Tiw+cal / °C
1
2
3
4
5
average
Table 3
Heat changes and specific heat capacity for the aluminum object and unknown metal object.
water and calorimeter
metal
aluminum
unknown
heat capacity
Cw+cal, J K -1
temperature change
∆T / K
metal
heat gained
Qw+cal / J
temperature change
∆T / K
heat lost
Qm / J
specific heat capacity
cm / J kg-1K-1