- Describe how the kinetic model accounts for the pressure of a gas.
- State that the pressure of a fixed mass of gas at constant temperature is inversely proportional to volume.
- State that the pressure of a fixed mass of gas at constant volume is directly proportional to its temperature measured in kelvins (K).
- State that the volume of a fixed mass of gas at constant pressure is directly proportional to its temperature measured in kelvins (K).
- Carry out calculations to convert temperatures in
^{o}C TO K and vice versa. - Carry out calculations involving pressure, volume and temperature of a fixed mass of gas using the general gas equation.
- Explain what is meant by the absolute zero of temperature.
- Explain the pressure-volume, pressure-temperature and volume-temperature laws qualitatively in terms of a kinetic model.

Aids to Understanding

Fluids

Gases and liquids are classified as fluids because they can flow. However two gas molecules
have ten times more space between than two liquid molecules and fill up whatever container they occupy.
This means gases can be easilly compressed and easilly expand with rising tempertures. This opens up opportunities for investigation in gases.
Namely; Volume and Pressure and Temperature and pressure.

P-V problem

Find an expression for the pressure of the combined spherical flasks when the valve is open. Suppose the temperature of the gas stays constant. The pressure in the smaller flask is zero when the
valve is closed. You may ignore any gas in the joining tube.

Suppose the lower flask has a radius exactly one half of the upper flask. By what ratio does the pressure decrease when the valve is open?

Proportionality

If the result of an investigation yields a straight line through the origin then the quantities we investigated are in direct proportion.
There are two conditions for direct proportionality.

i) Both quantities have to be zero at the same time.

ii) The quantities must change by the same factor. ie if the independent variable doubles or triples so does the dependent variable.

A direct proportion relationship is of the form Y = mx, ie V = IR or F = ma.

When we investigate temperature and pressure, when temperature is measured in degrees celcius we get a line of the form Y = mx + C. Where
Y is pressure and x is temperature. Although this expression allows us to make predictions it is not a direct proportion relationship so it becomes
difficult to combine the results of our gas investigations into one expression. The answer is to introduce a new temperature scale - the Kelvin scale.
Each one degree change in degrees celcius corresponds to a one degree change in kelvin. Note: 0 K is equal to -273.15. This value is known
as Absolute zero

P-V-T problem

This is a continuation of the above problem but now we extend it to include our knowledge of the temperature and pressure law.
By what ratio must the temperature increase if the pressure is to remain what is was before the valve was open?

P-V problem

How would you use this apparatus to find the volume of a marble? Suggest possible values and try to write your own problem.

Atmospheric Pressure

Although we don't notice we are a bit like fish. Where fish live in a sea or river of water we live in a sea of air. This
air is colliding with us in all directions and exerting a pressure. The pressure of the air, or air pressure, tends to squash
us but since we have air inside our bodies that tends to inflate us we are in equilibrium with the air outside. You may think
air pressure is quite small but remember the air that extends from the earth to where it merges with outer space is about
100 km. That is a lot of air pressing down on us (even if air density decreases with distance). This air pressure has been measured
to be about 100 KPa. This means air pressure can support a mass of 10, 000 kg sitting on a 1 m

The temperature - volume law

This law is sometimes called Charles Law. In this investigation we keep the pressure
of the gas constant as we increase the temperature. As the gas in the tube is heated it
is allowed to expand. The air pressure inside the tube always, but no more, supports
the same mercury blob. Thus the pressure exerted of the gas does not change.

The general gas equation

Since P ∝1/V and V ∝T and P∝T it follows that P_{1}V_{1}/T_{1} is equal to a constant value therefore
we can say that; P_{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2}.

This is known as the ** general gas equation **.

You are invited to work out the units of PV/T.

Suppose a fixed mass of gas is at a Temperature, T_{1}, Volume, V_{1} and Pressure P_{1}.
If the temperature decreases by a factor of 3 and the volume also decreases by a factor of 3, then what will
the ratio of P_{1}/P_{2} be?

The general gas equation and graphs

The graphs below summarise the results of our gas investigations. T_{1}, V_{1}, and P_{1} all indicate
that the activities took place at constant temperature, volume and pressure respectively.

You are invited to copy out these graphs and draw on them how they would change she if..

(i) The activity was completed at a temperature higher and lower than T_{1}.

(ii)The activity was completed at a volume higher and lower than V_{1}.

(ii)The activity was completed at a pressure higher and lower than P_{1}.

The gas laws and kinetic model

Suppose we have a container of gas
at atmospheric pressure and a temperature of
300K.
(i) Suppose the volume of the container falls by
one third and its temperature rises three times.
Calculate the new pressure of the gas.

(ii) Explain this result using the kinetic model.
A representative sample of answers will be posted here.

The lower grapgh shoes that pressure and volume are inversely proportional or equivalently pressure is directly proportional to 1/Volume. The gradient of this line (20 units) is the same whatever pair of points you choose. ie P

The subcripts 1 and 2 indicate the initial and final states of pressure and volume. You should be able to see that if we have any three of these quantities, it is easy to find a fourth.

The line is extrapolated until it cuts the temperature line when the pressure is zero. This occurs at -273

The graph shoes that temperature (in Kelvin) and volume are directly proportional. The gradient of this line is the same whatever pair of points you choose. ie T

Object, body or substance | Temperature (K) | Temperature (^{o}C) |
---|---|---|

Freezing Water | - | 0 |

Boiling Water | - | 373 |

Body Temperature | - | 37 |

A nice day | - | 23 |

Absolute Zero | 0 | - |

- Gas particles are like tiny hard balls
- When a gas particle strikes the surface of its container, an elastic collision occurs.
- The pressure depends on the frequency of collisions.
- The pressure depends on the force of the collisions
- The force of the collisions depends on the speed of the gas molecules.
- To increase the speed of the gas molecules we need to increase their kinetic energy, and this can only be done if we increase their temperature.