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Boyle’s Law
Introduction
Robert Boyle was born in Ireland and lived during the seventeenth century; he had considerable wealth, which allowed him to spend a great deal of it investigating various physical phenomena. He published the second edition of New Experiments Physico-Mechanicall, Touching the Spring of the Air and its Effects in 1662, which contained a description of the experiment that showed what we now call Boyle’s law.
Boyle’s law simply states that for a gas at constant temperature, the product of pressure and volume is a constant. That is:
PV = constant
If we take several readings at different volumes, then we expect the result:
P1V1 = P2V2
This experiment will verify this equation. Boyle’s apparatus consisted of a U-tube sealed at one end, into which he poured mercury and examined the volume of the trapped air as the amount of mercury was increased. Mercury, being both very heavy and liquid at room temperature, was ideal for the job.
The pressure from the weight of the mercury increased as the volume of air decreased. In the picture, the gas in the sealed end must be at atmospheric pressure as the level of the mercury is level. Think of it this way: if the forces acting on both ends of the mercury were not equal, then the mercury would move. As mercury is added, the gas in the sealed-off end becomes compressed.
The pressure on the gas in the sealed end is now equal to the atmospheric pressure plus the pressure from the weight of the mercury that is above the level on the left of the tube.
Robert Hooke was working for Boyle when this experiment was performed, and it was Hooke’s careful measurements that resulted in a table of observations that showed the relationship now known as Boyle’s law. Although not used here, it was Hooke who designed and made the vacuum pumps that Boyle used in his other experiments with gases and the atmosphere.
The objective
To verify Boyle’s law: that at constant temperature, the product of pressure and volume is a constant.
The apparatus
You will need:
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A 10-ml syringe
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A stand with adjustable clamp
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Weight cradle and set of weights
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A G-clamp
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A micrometer
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Some rubber tubing sealed off at one end
Assemble the apparatus as shown here:
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A syringe is held by a clamp, with a weight holder attached to the plunger so that a force can be applied to it changing the pressure. Notice that the syringe is closed off at the top with a length of rubber tube and a small clamp. The stand can be clamped to the table with the G-clamp to give it added stability. A ruler is placed behind the syringe so that the position of the plunger can be easily determined.
The variables
The pressure is the independent variable, and the volume is the dependent variable.
The Physics
The area of the plunger can be calculated from its radius using the formula:
A = πR²
The pressure can be calculated from the formula:
P = F/A
Where F, the force, is calculated from the mass times g, the acceleration due to gravity (9.81 m/s).
To calculate the pressure in the syringe, you need to take account of the standard atmospheric pressure of 101 kPa. The pressure of the gas inside the syringe is the difference between the standard atmospheric pressure and the pressure due to the weight, as calculated previously.
The method
Accurately measure the diameter of the plunger head with a micrometer. Make a note of your measurement. Seal off the end of the syringe with a short length of tubing and a small clamp. Alternatively, seal it off with some hard-setting glue. For weights of 200 g, 400 g, 600 g, 800 g, and 1000 g, read the volume as accurately as you can from the position of the plunger in the syringe.
The Video
Watch a video for the Boyle's Law e-practical here.
This shows how to use it and how to collect the data.
The E-Practical
Perform the experiment yourself, collect your own data, make mistakes and be able to correct them. The e-practical requires that your browser can run WebGL 2 (usually found on Windows browsers, safari on iOS, and various Mobile browsers, test with https://get.webgl.org/webgl2/). This link is for students and evaluation only, schools should purchase a site licence.
All the e-practicals will run on devices as small as a mobile 'phone. However, the best experience is on a PC using a mouse which gives very precise control, but if you are limited to a small device, consider using a stylus or a blue tooth mouse.
Measure the diameter of the plunger head by using the mouse wheel with the cursor over the barrel of the micrometer (or dragging if using onscreen controls). Turn the barrel with the wheel until it will not turn any further. At this point, the micrometer is gripping the plunger. Read the micrometer to get the diameter.
The weights can be altered by putting the mouse cursor over the weight cradle and using the mouse wheel.
You can zoom in and out using the plus and minus or Z and X keys. Measure the plunger position as shown here:
The Results
Create a table as follows but with your own data:
When you have completed the table, plot 1/V against the pressure. You should obtain a straight line which confirms the law.
Further Discussion
How do you think this experiment might be improved?
In particular, how do you think it could be made more accurate?
What do you think of Boyle’s original method?
This section is adapted from material developed by Dr Robert Lucas and is related to the book High School and Undergraduate Physics Practicals, published by CRC Press.