Latent Heat of Vaporization of Nitrogen
PURPOSE
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To measure the heat of vaporization of nitrogen using two different methods.
INTRODUCTION
The heat of vaporization for a substance is the amount of energy required to change a unit
mass of the substance from liquid to gas. It is usually given the symbol L (for latent heat) and is
measured in units of Joules/gram. To find the actual amount of energy, QV, added to a substance
in order to vaporize a mass of M grams, you simply multiply the heat of vaporization times the
mass of substance vaporized,
QV = ML .
(1)
QV is positive indicating that energy must be added to the substance to vaporize it. The
€
temperature at which nitrogen vaporizes
at one atmosphere of pressure is 77 K.
In Method #1, energy is added to the nitrogen in a “lump” by adding a piece of aluminum
to the sample of liquid nitrogen. You will measure how much liquid nitrogen evaporates as the
aluminum cools. The amount of energy that must be removed from the aluminum, dQ, to
decrease its temperature slightly by an amount dT is determined by the specific heat of
aluminum.
dQ = m c dT ,
(2)
where m is the mass of the piece of aluminum and c is the specific heat at constant volume or
constant pressure (for a solid the€two specific heats are virtually the same). dQ is negative if dT
is negative, meaning energy must be removed from the aluminum to decrease its temperature. In
order to find the total amount of energy, QC, removed from the aluminum in cooling it from
room temperature to 77 K, these small amounts of energy necessary to decrease its temperature
slightly must be added together (integrated).
T2
QC =
T2
∫ m c dT = m ∫ c dT ,
T1
T1
(3)
where T1 is room temperature and T2 is 77 K. Notice that the specific heat depends upon the
€ specific heat of aluminum at varying temperature is provided to you.
temperature. A table of the
Again, QC is negative. Since the energy to cool the aluminum comes from the vaporization of
nitrogen, QV + QC = 0.
In Method #2, energy is added to the liquid nitrogen at a known rate by passing a current,
I, through a resistor immersed in the liquid nitrogen. As current passes through a resistor, the
resistor heats up and imparts its energy to the nitrogen. The rate energy is added to the liquid
nitrogen (i.e. removed from the resistor) is given by the power, P, dissipated by the resistor,
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Latent Heat of Vaporization of Nitrogen
PC =
dQC
= −IV
dt
(4)
where t is time and V is the voltage across the resistor. PC is negative since energy is being
€
removed from the resistor.
Liquid nitrogen vaporizes in response to this steady influx of energy from the resistor.
Since the latent heat, L, is constant, this addition of energy results in steady rate of vaporization,
dM/dt,
dQV
dM
=L
dt
dt
(5)
This rate is positive and must equal in magnitude the power dissipated by the resistor, dQV/dt +
€
dQC/dt = 0.
PROCEDURE
The liquid nitrogen is in a sample container that can be placed on the mass balance. The
reading of the mass balance will decrease as liquid nitrogen vaporizes. This occurs even without
the aluminum or the resistor submerged because the container is not a perfect insulator. Your
experimental procedure must include recording mass balance readings both before and after the
aluminum is placed in the liquid nitrogen (Method #1) or the current is turned on (Method #2),
so you can separate out the various contributions to the decrease in the mass balance reading.
This is most easily done by recording the mass for a series of times read from a stopwatch. In
Method #2, keep the resistor submerged at all times, even when the current is not flowing. The
electrical circuit for Method #2 is shown below.
Q1. Why was it necessary to take mass vs. time data before adding the aluminum to the
liquid nitrogen (in method #1) or turning on the resistor (in method #2)?
Latent Heat of Vaporization of Nitrogen
9-3
Figure 1. The Resistor Circuit for Method #2.
WARNINGS
(1) Liquid nitrogen is very cold, so do not let it, or any object which has been cooled by it, touch
you or your clothing in any way.
(2) Do not drop anything in the liquid nitrogen, and wear safety glasses at all times.
(3) Place the piece of aluminum in the liquid nitrogen slowly, as it will cause the liquid nitrogen
to boil rapidly until equilibrium is reached. A piece of string is supplied for this purpose.
(4) The resistor can get very hot if it is not immersed in the liquid nitrogen. Pass current through
the resistor only when it is in the container and completely immersed in liquid nitrogen.
ANALYSIS
For both methods, make a graph of the mass balance reading as a function of time. Use
the slopes of these graphs before and after either the piece of aluminum is added or the current is
turned on to determine the amount of liquid nitrogen that vaporized due to the cooling of the
aluminum or the rate of liquid nitrogen vaporization due to the removal of energy from the
resistor.
In Method #1, you need to evaluate the integral in Equation 3. Table 1 gives the specific
heat at constant pressure of aluminum for several values of temperature. Enter this data into
Kaleidagraph and numerically integrate over the correct range of temperature using the
“Integrate - Area” option under the Macros menu.
Q2. How did you find the uncertainty in QC in method #1?
9-4
Latent Heat of Vaporization of Nitrogen
Use the results from steps 1 and 2 to find the heat of vaporization of nitrogen for both
methods. Include an error estimate based on the propagation of errors in the measured quantities.
Table 1. Specific heat of aluminum with
respect to temperature.
T(K)
cp (J g-1 K-1)
0
0.000
10
0.001
20
0.010
30
0.032
40
0.078
50
0.142
60
0.214
70
0.287
80
0.375
90
0.422
100
0.481
150
0.650
200
0.760
250
0.842
290
0.890
300
0.900
Q3. What were the values of the latent heat (with uncertainties) from both methods?
Q4. Are the results consistent? If not, what could be the reason?
Q5. How do your values compare with the actual value of 201 J/g for the latent heat of
nitrogen?
Pre-lab Question: What does the word “latent” mean (dictionary definition)? In your own
words, what is latent heat of vaporization? Don’t just quote the textbook! Why is the word
“latent” used for this property?
TO HAND IN:
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Mass vs. time graphs with best-fit lines for both methods
Answers to questions