# experiment 1500-13

```Otterbein University Department of Physics
Physics Laboratory 1500-13
EXPERIMENT 1500-13
BOYLE’S LAW AND GAY-LUSSAC’S LAW
NAME:
INTRODUCTION
The ideal gas law, PV = NkT, was put together from bits and pieces of information gleaned over
centuries. Robert Boyle, one of the first great modern experimental physicists (he was 15 years
older than Newton), observed in 1661 that for a gas a constant temperature, pressure and volume
are inversely related. About a hundred years later, Joseph Louis Gay-Lussac observed that for a
gas at constant volume, temperature and pressure are linearly related. Extrapolating to lower
temperatures, all gases would reach zero pressure at the same temperature, 273.15 C. If the
temperature is measured from this value, as on the Kelvin scale, Gay-Lussac’s law says that the
pressure is proportional to temperature at constant volume. In this lab, you will use modern
apparatus to verify the results of Boyle and Gay-Lussac, and determine the absolute zero of
temperature.
APPARATUS
LabPro interface, stainless steel temperature probe, gas pressure sensor kit, Thermos bottle of hot
water, bottle of ice water, 2 Tupperware bowls, 125 mL Erlenmeyer flask, rubber band or tape,
wall mounted barometer.
ACTIVITY A: BOYLE’S LAW
Gas pr essur e
sensor
1. For reference, consult the barometer on the wall, which is
calibrated to read the absolute atmospheric pressure in
mmHg, or Torr. At sea level, the average atmospheric
pressure is about 760 Torr, higher in fine weather and
lower if it is stormy. (The average pressure is about 3% less, or 737 Torr, at Otterbein’s
altitude of 850 ft.) The surface of the mercury has a curve called a meniscus; when you
of atmospheric pressure to kPa (1 kPa = 7.5 Torr).
2. Connect the gas pressure sensor to Ch 1 of the LabPro. Launch Logger Pro. Click on Data
Collection in the Experiment menu. Set the Mode is to “Events with Entry”. Type in
column name “Volume”, short name “Vol”, units “cc”. On this setting, Logger Pro will
collect pressure readings, and allow you to enter a volume measurement with each.
3. Record the reading of the pressure sensor:
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Otterbein University Department of Physics
Physics Laboratory 1500-13
If this is in significant disagreement with your barometer reading, you have a problem; consult
your lab instructor. On the other hand, a miscalibration of the pressure sensor by a few percent is
acceptable; it will not affect the outcome of your measurements.
4. Position the piston in the plastic syringe on the 10 mL mark. Attach the plastic syringe to the
gas pressure sensor, with a gentle half turn. Do not overtighten, or you may damage the
connector, but screw it firmly enough to make a good seal.
5. Click Collect. Click Keep when the pressure reading is stable. Enter the volume of the
syringe.
6. Change the volume of the syringe by about 2 mL. When the pressure reading is stable, click
Keep and enter the volume of the syringe. (If the pressure keeps decreasing, you have a leak
and will need to screw the syringe in a little tighter.) Repeat this procedure for a range of
syringe volumes from 20 mL to 5 mL. Do not collect any data above 210 kPa: the sensor
cannot measure any higher pressures. (Pressures over 400 kPa will damage the sensor.)
Click Stop when you are finished.
ANALYSIS
You should observe a clear trend in your data, indicating that pressure increases when volume
decreases. However, although you know the volume of air in the body of the syringe, the total
volume of air in your apparatus includes the volume in the neck of the syringe, as well as the
volume inside the pressure sensor. This useless extra volume is often referred to as dead volume.
Thus, you should expect your data to obey PVtot = P(V+V0) = const, where V0 is the dead volume.
This can be rewritten as V=const/PV0 which suggests that you plot your data as V vs. 1/P. From
the menu bar, click Data, New Calculated Column, Column Definition. For Long name and
short name, enter 1/p. For Units, enter kPa^(1). In the Equation box, type 1/“Pressure”.
(You must include the quotation marks; these tell Logger Pro that Pressure is the name of a
variable. Instead of typing “Pressure” you can select it from the Variables menu.) Finally,
click Done.
Click the label on the vertical axis of your graph window and select Volume from the window
that pops up. Similarly, click the label on the horizontal axis and select 1/p. Use the Regression
tool to fit a straight line to your data. Do your data fit a straight line, verifying Boyle’s law?
The y-intercept of your graph should be V0. What is value for V0? Is your value reasonable?
(You can’t see inside the sensor, but you can assume that the dead volume inside must be smaller
than the case, and ideally, much smaller.)
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Otterbein University Department of Physics
Physics Laboratory 1500-13
ACTIVITY B: GAY-LUSSAC’S LAW
1. Connect the stainless steel temperature probe to Channel 2. Close the current file and reopen
Logger Pro. You should see two graphs and two live readouts of temperature and pressure.
2. Delete the pressure graph, and enlarge the temperature graph to fill the whole page. Click on
the horizontal axis label and change it to pressure, so that you obtain a T vs. p plot.
3. Disconnect the syringe from the gas pressure sensor, and connect the tube from the rubber
stopper in the pressure sensor kit. The third “hole” is blind, .i.e. closed at its lower end.
Make sure your Erlenmeyer flask is absolutely dry inside; the vapor pressure of water has a
strong temperature dependence, and will greatly affect the results of this experiment. Secure
the rubber stopper in the opening of the flask. For the time being, leave the valve open on
the stopper.
4. Live readouts of the temperature and the pressure appear at the bottom of the screen. Record
the room temperature and pressure:
__________________
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5. Place the flask inside the Tupperware container. Secure the flask to the container with a
rubber band or tape it to the container; this will keep the flask from floating out of the tub
when you fill it with water.
6. If your Thermos bottles do not have hot water and ice water in them, ask your lab instructor
to fill them now.
7. Leave the valve on the stopper open. Pour hot water into the container outside the flask,
being careful not to get any water in the flask. After you have you have filled the container
up to the neck of the flask, close the valve.
8. Check that the data collection is set to “Selected Events” mode, see Activity A, point 2. In
this mode, Logger Pro will record a data point whenever you click the Keep button. You will
not have to manually enter any data in this portion of the lab. Click Collect.
9. Watch the readouts at the bottom of your screen. Give the flask and the temperature probe a
swish and a swizzle to ensure that the probe, water and flask are all in thermal equilibrium.
When the pressure and temperature settle down, click the Keep button. You must be very
careful to wait for the system to reach equilibrium to get the best results from this lab.
10. Carefully pour out about a fifth of the hot water in your tub, and replace it with cold water.
Give the flask and the temperature probe another good swizzle to ensure the water is in
equilibrium. Again, wait until the live readouts at the bottom of the screen settle on a value
and click the Keep button.
11. Repeat this procedure four more times to collect data at different temperatures (you should
have a total of six data points at the end of this step).
12. Pour out all of the water in your tub, and replace it with ice water. Collect one more data
point at this temperature.
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Otterbein University Department of Physics
Physics Laboratory 1500-13
ANALYSIS
1. Use the linear Regression tool to fit a straight line to your data. Is a straight line a good fit?
Print your plot and attach it.
2. Although it’s a large extrapolation from room temperature, the y-intercept of your graph is
your estimate of the absolute zero of temperature. How many degrees off is it from the value
273.15 C measured by other experimenters?
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