1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Purpose
• Understand how the total energy in a closed system
is conserved during heat exchange.
• Learn how to determine specific heat capacities of
certain materials.
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
The Heat Capacity of an Object
Amount of heat (energy) that needs to be added to the
object in order to raise its temperature by 1 degree Kelvin.
Q  C T  C T final  Tinitial 
Heat added
(in Joules)
Heat capacity
(in Joules/Kelvin)
If
If
Q>0
Q<0
then Tfinal > Tinitial
then Tfinal < Tinitial
Change in Temperature
(in Kelvin)
(temperature rises)
(temperature drops)
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
The heat capacity depends on:
 Type of Material
 Amount of the material (more water has more heat
capacity……… you need more energy to raise its
temperature………
The specific heat capacity is defined as
J
and has units of kg K
cal
or
g K
C
c
mass
(1 cal  4.19 J )
The specific heat capacity only depends on the material,
not on the amount of the material.
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
The Specific Heat Capacity
Amount of heat (energy) per unit mass that needs to be added to
a material in order to raise its temperature by 1 degree Kelvin.
Q  c m T  c m T final  Tinitial 
Heat added
(in Joules)
Specific Heat capacity
Change in Temperature
(in Kelvin)
mass of the object
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Example and Implications of Specific Heat Capacity
cwater  1
cal
J
 4.180
g K
g K
A calorie is defined as the amount of heat that needs to be added to 1
gram of water in order to raise its temperature by 1 degree Kelvin.
Water has a relatively high heat capacity, which is important in biology and engineering:
Prevents your body (= mostly water) from heating up too quickly during exercise (an apple
that contains 60Kcal of energy has the potential to raise the temperature of a 60Kg
person by only
T = Q/(c*m) = 60000cal/(1 cal g-1K –1 * 60000g)=1Kelvin
(assuming all the energy in the apple would go to heat and none to work performed)
Is a good coolant for engines (can absorb a lot of heat without having its temperature rise a
lot.
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Heat Transfer Between Two Objects
(assume no heat is lost to the environment)
Before contact:
After reaching
thermal equilibrium
they both have the
same temperature
m1
c1
T1, initial
m1
c1
T1, final
m2
m2
c2 T2, initial
c2 T2, final
T1, final = T2, final = Tfinal
Given: m1, m2, c1, c2, T1,initial, T2,initial
(Tfinal unkown)
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Q1  c1 m1 T final  T1,initial 
Q2  c2 m2 T final  T2,initial 
Because no heat is lost to (or gained from) the environment:
Q1  Q2  0
The originally colder object gains energy (a positive Q)
The originally hotter object looses energy (a negative Q)
c1 m1 T final  T1,initial   c2 m2 T final  T2,initial   0
 Solve for Tfinal
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 1: Calibration of Temperature Probe
Themocouples are very easily built temperature sensors.
Two dissimilar conductors touching each other produce a voltage V that
changes with temperature T.
Over certain temperature ranges T is proportional to V and one can calibrate
them by finding the voltage for two temperature points and then making a
linear approximation. Thermocouple voltages can then be related to
temperature.
V
Vhot
Vcold
Two calibration points
Tcold
Thot
T
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 1: Calibration of Temperature Probe
Alcohol thermometer (read off
temperature here)
Temp. Probe
750 Interface
Use ice bath and warm water bath for the two calibration points
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 2: Determining the Power Output of the Heater
Styrofoam cup filled with 150
ml water. Make sure heater
doesn’t touch styrofoam
!!!!!
Stand +
clamp
heater
Red LED: Heater is ON
Heater
Switch Box
Temp. Probe
Computer:
Capstone
Switches
Heater on/off
750 Interface
Make sure this is plugged in the right way (ground to ground); ground is marked on tape
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 2: Determining the Power Output of the Heater
Observe total temperature change T due to heating:
First part with heater on
Temperature
T
After switching heater off.
time
Turn Heater off (Turn off “Signal Generator” in Capstone)
Heater on
t
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 2: Determining the Power Output of the Heater
Click here
to open
signal
generator
panel
• First click on “Auto” : This ensures that when
you hit “Record” the heater automatically starts
with the recording.
• Click on “Record” (lower left corner of
Capstone).
• After a fixed (known) amount of time stop just
the heater (but not temperature measurement)
by clicking “OFF”.
• To stop temperature recording, click on the
“Stop” button in the lower right corner.
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 2: Determining the Power Output of the Heater
Power = Energy / time = c m T / t
This is the heat/energy
given off to the water
( = “Q” )
Compare your result to the power rating written
on the heating element.
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 3: Determine Specific Heat Capacity of Isopropyl Alcohol
Design an experiment to measure c isopropyl alcohol
Use your measured power rating of the heating element.
Caution: Isopropyl alcohol is a flammable liquid. If you accidentally
spill it over a power outlet, do not unplug the equipment. Sparks may
ignite the alcohol!
• DO NOT DRAIN THE ISOPROPYL ALCOHOL INTO THE
SINK !!!!! It is illegal to do that and we also do not want to waste
the alcohol – it costs money.
• Instead, please pour it back into the container from which you
got it.
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 4: The Transfer of Heat
Caution: This experiment uses liquid nitrogen, which is extremely
cold. Follow the safety instructions!
Step 3:
Monitor
temperature
Step 2:
Put cold brass (-197ºC)
into water.
Step 1:
Cool brass in the LN2
(wait until bubbling stops)
Brass disc
on a string
Water at Room
Temperature
Liquid nitrogen (LN2)
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Activity 4: The Transfer of Heat
Step 4: Determine the specific heat capacity of brass
Step 5: Compare your value of cbrass to that in the literature
(you can surely find that value on the internet)
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Hints
• Do not be surprised if the power rating of the heater element
disagrees with what you measured. When we measured the
resistance of the heating elements with wires, some were as
high as 2 Ohms.
• Therefore, a more realistic power rating may be about

U
12 V 
P

 72 Watt
R
2
2
2
• …and it may be even lower if the supplied voltage is less than
12 Volts (on some of the heater boxes)  That’s why you need
to use your measured power rating in Activity 3, not the official
rating.
1809: The Relationship Between Heat and Temperature
Physics 1809 Minilab 2: Heat and Physics
Temperature
Liquid Nitrogen Safety
•
•
Wear goggles when using liquid nitrogen.
Pour liquid nitrogen slowly and very carefully.
•
Do not deliberately spill liquid nitrogen.
•
When putting the brass object into liquid nitrogen, suspend it on a
string and carefully lower it into the liquid nitrogen (the nitrogen will
boil rapidly).
•
Do not touch liquid nitrogen or metal surfaces that are in direct contact
with liquid nitrogen.
•
Never put liquid nitrogen into a closed container (except into specially
designed containers with pressure relief and safety valves). It will
explode and you may be seriously injured or killed by the exploding
fragments.
•
When carrying liquid nitrogen to your table, walk carefully and make
sure nobody bumps into you (or you into them).
•
When done with your liquid nitrogen, you can carefully pour it back
into the dewar.