Lesson 41 42 notes – Boyle’s Law
Objectives
Be able to state Boyle’s law.
Outcomes
Be able to state Boyle’s law;
Be able to describe an experiment that demonstrates Boyle’s Law.
Boyle’s Law
Boyle’s Law states that the pressure of a gas is inversely
proportional to its volume.
Boyle’s law and number of molecules
Two ways to double gas
pressure
N molecules in volume V
cram in more molecules
increase N
squash the gas
decrease V
piston squashes up same molecules into
half the volume, so doubles the number per
unit volume
N molecules
molecules in box:
pressure due to impacts
of molecules with walls
of box
add extra molecules to double the number,
so double the number per unit volume
same:
number of molecules
per unit volume
number of impacts on
wall per second
pressure
pressure proportional to 1/volume
p  1/V
2N molecules in volume V
pressure proportional to number of molecules
pN
If.... pressure is proportional to number of
impacts on wall per second
Then.... pressure is proportional to number of
molecules per unit volume
and if.... number of impacts on wall per second
is proportional to number of molecules per unit
volume
p = constant  N/V
Boyle’s law in two forms
pV = constant  N
p = constant  N/V
Boyle’s law says that pressure is proportional to crowding of molecules
Boyle’s law and gas density
1
2
4
3
pressure p
volume V
mass m
density d
Boyle’s law:
compress gas to half volume:
double pressure and density
1
2
4
3
pressure 2p
volume V/2
mass m
density 2d
half as much gas in half volume:
same pressure and density
1
2
4
3
double mass of gas in same volume:
double pressure and density
pressure p
2
3
pressure 2p
volume V
mass 2m
density 2d
volume V/2
mass m/2
density d
push in
piston
1
4
pump in
more air
temperature constant in each
Boyle’s law says that gas pressure is proportional to density
Boyle’s Law Experiment
You need to measure how the volume of a fixed number of particles affects the pressure.
Squeezing these particles into a smaller and smaller volume results in more and more
collisions with the walls, giving a higher pressure. However, you will only get a true
relationship between pressure and volume if the number of particles stays the same: you
need to make sure that no molecules escape. Rough and ready results can be obtained by
using syringes, but these leak, so more precise ways have evolved – sealing off a volume of
gas behind a liquid makes for a good seal. It is the measurement of volume that turns out to
be the difficult one to get right. You may be able to set up a slicker arrangement using
automated data capture, but you will need to take great care to measure the volume, ensuring
the equivalent of a leak-proof syringe, where you can measure the position of the plunger or
piston.
Compressing a gas will warm it up and vice versa, so after changing the volume leave
sufficient time for the temperature to return to its original value.
A traditional solution
sample of air
0
101300 Pa
5
10
15
20
oil to transmit pressure
Extension
The Pressure Law
Pressure and volume of gases increasing with temperature
Constant volume
Constant pressure
1
2
4
3
pressure p
45.1
45.1
volume V
T/C
T/C
heat gas:
pressure
increases
–273
heat gas:
volume
increases
0
temperature/C
–273
0
temperature/C
Pressure and volume extrapolate to zero at same temperature –273.16 C
So define this temperature as zero of Kelvin scale of temperature, symbol T
0
273
temperature/K
pressure proportional to Kelvin temperature
273
temperature/K
volume proportional to Kelvin temperature
pT
VT
0
Pressure and volume proportional to absolute temperature
Charle’s Law
Charles's Law states that the volume of a given amount of dry ideal gas is
directly proportional to the Kelvin Temperature provided the amount of gas
and the pressure remain fixed.
When we plot the Volume of a gas against the Kelvin temperature it forms a
straight line. The mathematical statement is that the V / T = a constant. For
two sets of conditions the following is a math statement of Charles's Law:
V1 / T1 = V2 / T2