# Heat Capacity Heat of fusion by mtc13769

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```									Practical Class Physics                                                     Hochschule Bonn-Rhein-Sieg/ FB 05
Stand 02/09

Heat Capacity/ Heat of fusion

Preparation
Answer the following questions and bring along your notes to the practical course!
• Draw the temperature curve when ice is heated from –10°C to +120°C.
• Why is it important to keep the calorimeter closed during the measurements?
• Why is the heat capacity of the calorimeter taken into account?
• Why is it important to keep the total filling volume of the calorimeter constant?
• What is the specific heat capacity of water and what is the heat of fusion of ice? Give
literature values.
• Solve equation (5) for the calorimeter constant CCal
• Equalize formula (6) and (7) and solve for heat of fusion (qF)

Basics
The quantity heat Q is given by the amount of energy needed to heat or cool a body of mass
m by ΔT. Q is proportional to the mass m and to the resulting temperature difference. The
constant of proportionality is called specific heat capacity c:

Q = m ⋅ c ⋅ ΔT                                                        (1)

The heat capacity C is defined as the amount of heat needed to heat the body by 1K:

C = m⋅c                                                               (2)

If two or more bodies of different temperature are put into close contact they exchange heat
until the same temperature is reached. According to the law of conservation of energy the
amount of heat released by the body of higher temperature equals the amount of heat gained
by the body of lower temperature. The mixing rule of Richman is:

Qreleased = Q gained                                                  (3)

c1 ⋅ m1 ⋅ ΔT1 = c 2 ⋅ m2 ⋅ ΔT2                                        (4)

Fig. 1 shows a calorimeter, which can be used for measuring the
heat transfer of liquids and solids. Calorimeters are usually well
insulated by evacuated double walls.
Since the temperature of the calorimeter changes during filling, the
heat capacity of the calorimeter itself has to be taken into account:

c1 ⋅ m1 ⋅ ΔT1 = (c 2 ⋅ m2 + C Cal ) ⋅ ΔT2                             (5)

Q       Amount of heat in J (Joule)
ΔT      Temperature difference of starting temp and end up temp in K (Kelvin)
m       Mass in kg
c       Specific heat capacity in J/(kg K)
C       Heat capacity in J/K
C Cal    Heat capacity of the calorimeter in J/K

If a phase transition like melting or vaporization takes place during the temperature change,
energy is required for the phase transition.
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Practical Class Physics                                                   Hochschule Bonn-Rhein-Sieg/ FB 05
Stand 02/09

The temperature stays constant during the transition. The amount of energy required for the
phase transition from solid to liquid is called heat of fusion.

Ice of 0°C is melted in a calorimeter filled with hot water. Heat is transferred from the hot
water to the ice until the ice is completely melted. Also a small amount of heat is transferred
from the calorimeter to the ice.

The amount of heat released from the calorimeter and the water is:

Qreleased = (CCal + mW ⋅ cW ) ⋅ (T1 − T2 )                          (6)

The amount of heat absorbed by the ice is:

Q gained = m Ice ⋅ q F + m Ice ⋅ cW ⋅ (T2 − Tmelting )              (7)

T1         starting temperature
T2         end up temperature
Tmelting   melting temperature of the ice
mIce       mass of the ice
mW         mass of the water
cW         specific heat capacity of the water = 4,1861 kJ/(kg K)
CCal       heat capacity of the calorimeter
qF         heat of fusion

Problem
•     Determine the heat capacity of the calorimeter you will use in your experiment.
•     Determine the specific heat capacity of a solid (aluminum, iron or brass) with the mix-
ing rule of Richman. Take the heat capacity of the calorimeter you determined before.
•     Determine the heat of fusion of ice in a calorimeter with the mixing rule of Richman

Procedure and evaluation

Heat capacity of the calorimeter (3 runs)
The heat capacity of the calorimeter can be determined from mixing experiments.
A certain amount of hot water is mixed with cold water in the calorimeter.
When the temperatures before and after mixing are measured, the calorimeter constant could
be calculated with equation (5)

Remark: The calorimeter constant depends on the filling level of the calorimeter.
Make sure that the filling of the calorimeter is similar during all runs.

•     Take the calorimeter and measure its weight (complete with top!)
•     Put a certain amount of water at room temperature into the calorimeter. Close the calo-
rimeter and measure the starting temperature of cold water
•     Determine the exact amount of water by weighing the filled calorimeter. The differ-
ence in mass gives you the mass of cold water
•     Heat up a certain amount of water to approximately 50°C (Note the start up temp of
warm water exactly)
•     Put the warm water to the cold water into the calorimeter and stir the content until a
mixing temperature is reached

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Practical Class Physics                                          Hochschule Bonn-Rhein-Sieg/ FB 05
Stand 02/09

•   Note the end temp for hot and cold water
•   Determine the mass of the added warm water by weighing the filled calorimeter.
•   Calculate the heat capacity of the calorimeter for each measurement
•   Determine the average value and the standard deviation for the calorimeter constant
•   Don’t forget the error discussion

Specific heat capacity of solids (3 runs)
A piece of aluminum (brass or iron) is heated up. Then it is placed into a calorimeter, filled
with water. The specific heat capacity of aluminum can be determined with equation (5) when
the mixing temperature has been measured.

•   Measure the mass of aluminum (brass or iron) with a balance.
•   Heat up the piece of aluminum in a water bath up to approx. 70°C (Note the starting
temp of aluminium exactly!)
•   Take the calorimeter and measure its weight
•   Put a certain amount of water at room temperature into the calorimeter.
•   Determine the exact amount of water by weighing the filled calorimeter. The differ-
ence in mass gives you the mass of water
•   Measure the starting temperature of water in the closed calorimeter
•   Dry the heated up piece of aluminum (brass or iron) and put it into the calorimeter
filled with water. Close the calorimeter.
•   Wait until the mixing temperature is arrived and note the end up temp for water and
the piece of aluminium
•   Take the calorimeter constant from your experiment before and calculate the specific
heat capacities of aluminum for each measurement
•   Determine the average value and the standard deviation and compare your results to
the literature values
•   Discuss your results and explain the deviation to literature values. (error discussion)

Heat of fusion (3 runs)
The amount of energy required for the phase transition from solid to liquid is called heat of
fusion and could be determined in this experiment, by mixing some ice with water.

Remark for mixing ratio: Three quarters of water with one quarter of ice

•   Heat 0,8-1,0 L water to approx. 40°C (adequate for 3 runs!)
•   Take the calorimeter and measure its weight (complete with top!)
•   Weigh in a certain amount of warm water into the calorimeter
•   Close the calorimeter and note the starting temperature in the calorimeter
•   Dry some ice and put it into the calorimeter, filled with warm water.
•   Determine the exact amount of ice by reweighing the filled calorimeter
•   Stir the content of the calorimeter until the ice is melted (keep the calorimeter closed!)
•   Note the end up temperature
•   Equalize formula (6) and (7) Solve the equation for qF
•   Take the calorimeter constant from your experiment before and calculate the heat of
fusion of water for each measurement
•   Determine the average value and the standard deviation and compare your results to
the literature values
•   What are the largest errors of the measurements? How could one improve the experi-
ment?
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