Latent Heat - DOC by DV8sg3Q

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Introduction
The amount of heat transfer per unit mass required to produce a phase change (with no temperature
change) in a substance is called the latent heat. If the phase change is from solid to liquid (or vice
versa), then it is called the latent heat of fusion. If the phase change is from liquid to gas (or vice versa),
then it is called the latent heat of vaporization. This relation is given by the following equation:

[1] Q = ±mL
Q = heat (J)
m = mass of the substance (kg)
L = latent heat (J/kg)

The sign in the equation must be put in manually to indicate the direction of the phase change. The
purpose of this lab is to test the theoretical value of heat of fusion for water.

In this experiment, we will throw ice cubes into hot water. We can use the principle of conservation of
energy along with the accepted value of the specific heat capacity of water and experimental values of
temperature and mass to calculate the experimental value of heat of fusion for water. A conservation
of energy statement for this experiment can be written as follows:

[2] ΣQ = 0

In this experiment, the ice will melt and then change its temperature to the equilibrium value. The hot
water will simply change its temperature to the equilibrium value. These three processes need to be
taken into account in equation [2]. Also, recall that the relationship between heat and temperature
change is Q = mcΔT. Equation [2] can be written more specifically as follows:

[3] miLf + micw(Teq – Ti) + mhcw(Teq – Th) = 0
mi = mass of ice
Lf = heat of fusion for water
cw = specific heat capacity of water
mh = mass of hot water
Teq = equilibrium temperature
Ti = initial temperature of ice
Th = initial temperature of hot water

Equation [3] can be solved for Lf in terms of known or measurable quantities. This is left as an exercise
for the student.
Experimental Procedures

1) Measure and record the mass of a Styrofoam cup and lid. Fill the cup about half full of hot tap
water and measure the total mass with the lid placed next to the cup. Calculate the difference to
obtain the mass of the water.

2) Measure and record the initial temperature of the water once the temperature is fairly steady.

3) Using a towel, dry off cubes of ice and put them in the hot water. Add 3 to 6 cubes and cover.
Occasionally gently shake the cup until the temperature is steady. Record the final equilibrium
temperature.

4) Measure the final mass of the cup and water. Calculate the difference between this value and your
previous measurement to obtain the mass of the ice.

5) Use equation [3] to calculate the latent heat of fusion for water. Compare your experimental result
to the theoretical value of (3.34 ± 0.01) E5 J/kg. The specific heat of liquid H2O is (4190 ± 15)
J/(C° kg).

6) Complete this experiment two more times with a different initial temperature of water, different
amount of hot water, or different amount of ice.

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