A sample of helium occupies a volume of 160
at 100 kPa and 25
C. What volume will it occupy if the pressure is adjusted to 80 kPa and if the temperature remains unchanged?
V
= 160 cm
and V
= ?
p
= 100 kPa and p
= 80 kPa
Because the temperature of the gas stays the same, the following equation can be used:
If the equation is rearranged, then
The volume occupied by the gas at a pressure of 80kPa, is 200 cm
The pressure on a 2.5 l volume of gas is increased from 695 Pa to 755 Pa while a constant temperature is maintained. What is the volume of the gas under these pressure conditions?
It is not necessary to convert to Standard International (SI) units in the examples we have used above. Changing pressure and volume into different units involves
multiplication . If you were to change the units in the above equation, this would involve multiplication on both sides of the equation, and so the conversions cancel each other out. However, although
SI units don't have to be used, you must make sure that for each variable you use the
same units throughout the equation. This is not true for some of the calculations we will do at a later stage, where SI units
must be used.
Boyle's law
An unknown gas has an initial pressure of 150 kPa and a volume of 1 L. If the volume is increased to 1.5 L, what will the pressure now be?
A bicycle pump contains 250 cm
of air at a pressure of 90 kPa. If the air is compressed, the volume is reduced to 200 cm
. What is the pressure of the air inside the pump?
The air inside a syringe occupies a volume of 10 cm
and exerts a pressure of 100 kPa. If the end of the syringe is sealed and the plunger is pushed down, the pressure increases to 120 kPa. What is the volume of the air in the syringe?
During an investigation to find the relationship between the pressure and volume of an enclosed gas at constant temperature, the following results were obtained.
Volume (cm
)
Pressure (kPa)
40
125.0
30
166.7
25
200.0
For the results given in the above table, plot a graph of
pressure (y-axis) against the
inverse of volume (x-axis).
From the graph, deduce the relationship between the pressure and volume of an enclosed gas at constant temperature.
Use the graph to predict what the volume of the gas would be at a pressure of 40 kPa. Show on your graph how you arrived at your answer.
(
IEB 2004 Paper 2 )
Charles' law: volume and temperature of an enclosed gas
Charles' law describes the relationship between the
volume and
temperature of a gas. The law was first published by Joseph Louis Gay-Lussac in 1802, but he referenced unpublished work by Jacques Charles from around 1787. This law states that at constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in kelvin) increases or decreases. Another way of saying this is that temperature and volume are
directly proportional .
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