1. Physics 12
Calorimetry

2. Objectives Define specific heat capacity.
Solve problems involving specific heat capacities.
Explain the difference between solid, liquid, and gaseous phases.
Explain in terms of molecular behavior why temperature does not change during a phase change.
Define latent heat.
Solve problems involving latent heats.

3. Activities
Worksheet
Lab demonstration: Determining the specific heat capacity of a substance
Lab demonstration: Determining the latent heat of a substance
Design lab: Design a homemade calorimeter and test it

4. Specific heat capacity
If heat flows into an object, its temperature rises.
What factors might affect the magnitude of the temperature change?

5. Specific heat capacity
The amount of energy Q required to change the temperature of a given material is proportional to the mass m of the material and to the temperature change ΔT, shown by the simplistic expression:
Q = mc ΔT
where c is the characteristic of the material called its specific heat capacity

6. Specific heat capacity
A high specific heat capacity means that more energy is required to achieve the same temperature change, i.e. it is more “difficult” to raise the temperature of that material.
If a material is a good heat conductor (e.g. metals) would you expect it to have a high or low specific heat capacity?

7. Specific heat capacity
Specific heat capacities of specific substances
Substance
Specific heat capacity, c / Jkg-1°C-1
aluminum
900
copper
390
iron or steel
450
lead
130
wood
1700
water (ice)
2100
water (liquid)
4186
water (steam)
2010
human body (average)
3470

8. Specific heat capacity
Q / J
m / kg
c / Jkg-1C-1
ΔT / °C or °K ?
increased
constant

9. Specific heat capacity
How much heat input is needed to raise the temperature of an empty 20-kg vat made of iron from 10C to 90C?
What if the vat is filled with 20 kg of water?

10. Specific heat capacity
720 kJ
7400 kJ

11. Specific heat capacity
You accidentally let an empty iron frying pan get very hot on the stove (approx. 200C). What happens when you dunk it into a few inches of cool water in the bottom of the sink? Will the final temperature be midway between the initial temperatures of the water and pan? Will the water start boiling? (Assume the mass of the water is roughly the same as the mass of the pan.)

12. Calorimetry
In discussing heat and thermodynamics, we shall often refer to systems.
What is the difference between open, closed, and isolated systems?

13. Calorimetry Open system Closed system Isolated system
Mass and energy may leave and enter
Closed system
Energy may leave and enter but mass may not
Isolated system
Neither mass nor energy may leave or enter

14. Calorimetry
We will often make the assumption that the systems we are dealing with are isolated.
Why is this necessary?

15. energy out of one part = energy into another part
Calorimetry
In an isolated system, heat lost by one part of the system is equal to the heat gained by another part:
heat lost = heat gained or
energy out of one part = energy into another part

16. Calorimetry
If 200 cm3 of tea at 95C is poured into a 150-g glass cup initially at 25C, what will be the common final temperature T of the tea and cup when thermal equilibrium is reached, assuming no heat flows to the surroundings?

17. Calorimetry
T = 86C Would this be the case in the “real world”?

18. Calorimetry
The exchange of energy (as shown in the previous example) is the basis for the technique known as calorimetry.
Calorimetry is the quantitative measurement of heat exchange.
A calorimeter is used.

19. Calorimetry
A simple water calorimeter

20. Calorimetry
An engineer wishes to determine the specific heat of a new metal alloy. A kg sample of the alloy is heated to 540C. It is then quickly placed in 400 g of water at 10.0C, which is contained in a 200-g aluminum calorimeter cup. The final temperature of the system is 30.5C. Calculate the specific heat of the alloy.

21. Calorimetry
c = 500 Jkg-1C-1

22. where the two substances share a final temperature
Calorimetry
In order to determine the specific heat of a particular substance, the following expression is used:
Qlost = Qgained
m1c1ΔT1 = m2c2 ΔT2
where the two substances share a final temperature
Thus, all other quantities except one must be measured or known.

23. Phase change
Recall that matter most commonly exists in three states: solid, liquid, and gas.
What are the differences between these three states (or phases) in terms of molecular structure and motion?

24. Phase change Shape Volume Particle motion solid liquid gas
Comparison of the three common phases of matter (on Earth)
Shape
Volume
Particle motion
solid
liquid
gas

25. same as liquid but quicker
Phase change
Comparison of the three common phases of matter (on Earth)
Shape
Volume
Particle motion
solid
definite
vibrational
liquid
indefinite
rotational
translational
gas
same as liquid but quicker

26. Phase change
When a material changes phase from solid to liquid or liquid to gas, a certain amount of energy is involved in this change of phase.

27. Phase change
Temperature as a function of heat added to 10.0 g of ice

28. Phase change
The heat required to change a substance from solid to liquid is called latent heat of fusion.
The heat required to change a substance from liquid to gas is called the latent heat of vaporization.
Values for latent heats will vary depending on the substance.

29. Phase change Latent heats Substance Heat of fusion / kJkg-1
Heat of vaporization /
oxygen 14
210
ethyl alcohol
104
850
water
333
2260
iron
289
6340

30. Phase change
What factors might affect the amount of energy needed to change the phase of a substance?

31. where m is the mass of the substance and L is the latent heat
Phase change
The heat involved in a change of phase Q depends not only on the latent heat but also on the total mass of the substance, i.e.
Q = mL
where m is the mass of the substance and L is the latent heat

32. Phase change
How much energy does a freezer have to remove from 1.5 kg of water at 20C to make ice at –12C?

33. Phase change
6.6 x 105 J

34. Phase change
At a reception, a 0.50-kg chunk of ice at –10C is placed in 3.0 kg of tea at 20C. At what temperature and in what phase will the final mixture be? The tea can be considered as water. Ignore any heat flow to the surroundings, including the container.

35. Phase change
T = 5C

36. Phase change
The specific heat of liquid mercury is 140 Jkg-1C-1. When 1.0 kg of solid mercury at its melting point of –39C is placed in a 0.50-kg aluminum calorimeter filled with 1.2 kg of water at 20.0C, the final temperature of the combination is found to be 16.5C. What is the heat of fusion of mercury in Jkg-1?

37. Phase change
L = 11 x 103 Jkg-1

38. Objectives Define specific heat capacity.
Solve problems involving specific heat capacities.
Explain the difference between solid, liquid, and gaseous phases.
Explain in terms of molecular behavior why temperature does not change during a phase change.
Define latent heat.
Solve problems involving latent heats.

39. Measuring specific heat
Data collection
mass of metal
initial temperature of metal
mass of calorimeter
mass of calorimeter + water
initial temperature of water
final temperature

40. Measuring specific heat
Data processing
Include propagation of uncertainty
mass of water
ΔT of water
ΔT of metal

41. Measuring specific heat
Data processing
Include propagation of uncertainty
Q = mcΔT
Q (lost) = Q (gained)
mass of water
ΔT of water
ΔT of metal

42. Measuring specific heat
Homework
Write a conclusion and evaluation of the lab activity
Design a homemade calorimeter using the materials available. Try to minimize the amount of energy lost to the surroundings.
You will use this calorimeter for the next lab activity. The calorimeter with the smallest percent discrepancy gets bonus points.

43. Measuring latent heat of fusion
Data collection
mass of cup 1
mass of cup 1 + water
mass of cup 2
mass of cup 2 + ice
initial temperature of ice
initial temperature of water
final temperature

44. Measuring latent heat of fusion
Data processing
mass of water
ΔT of water
mass of ice
ΔT of ice

45. Measuring latent heat of fusion
Homework
Complete your data processing.
Make sure to include a sample calculation that shows the propagation of uncertainty.
Write a conclusion for your data, is the known value for the latent heat of fusion of water within your range of uncertainty?