The pressure, volume and temperature of a gas all affect one another. This would make the results of an experiment to investigate changes in all three at once complicated to understand. This problem is overcome by making one of them stay constant, whilst the relationship between the other two is investigated.

# Boyle’s Law- Volume and Pressure

This Law is about the variation of (a fixed mass of gas) volume with the pressure of a gas at steady temperature. The apparatus shown in the diagrams below may be used to find how the volume of a fixed mass of gas varies with pressure at a constant room temperature.

A syringe can be compressed to increase the pressure which is measured using a pressure sensor. The fixed mass of gas, usually air is trapped in the syringe, and its volume read from the scale.

Alternatively a foot or bicycle pupil is used to increase the pressure which is measured on the Bourdon Gauge. The fixed mass of air is trapped in the capillary tube by a bead of mercury, and its volume measured on the scale.

**How Pressure is related to volume for a constant mass and temperature of gas**.

Pressure (kPa) | 100 | 111 | 125 | 143 | 167 | 250 |
---|---|---|---|---|---|---|

volume of air column(cm 3 ) | 50 | 45 | 40 | 35 | 30 | 20 |

Use the results to show a relationship |

It is found that when the pressure in increased the volume of the gas decreased so that:

pressure × volume = constant

*p × V = k*

###### Boyle’s Law states that: *For a *__fixed mass of gas__ at __constant temperature__ the pressure is inversely proportional to the volume. *i.e. the pressure multiplied by the volume stays constant, provided the temperature does not change.*

*For a*

__fixed mass of gas__at__constant temperature__the pressure is inversely proportional to the volume.### Kinetic theory of Boyle’s law

The pressure of a gas is caused by the molecules hitting the walls of the container. Reducing the volume results in a shorter distance between the walls and so the number of molecules hitting the walls increases- resulting in increased pressure.

# The Pressure Law (Gay Lussac Law)

This law looks at the variation of pressure with temperature at constant volume. The apparatus shown below may be used to find how a fixed mass of gas, at constant volume varies with temperature.

The air is contained in a round bottom flask, which has a constant volume, and the pressure is measured using the pressure sensor attached to the flask by a short tube. It is important to have a short tube so that the temperature in the whole system is equal at any point. The round bottom flask is placed in a water bath which is used to vary the temperature of the water, and hence the air in the flask. Recent results have shown that the thermometer is best placed in the water bath as this gives more accurate results for the temperature of the air in the flask. Placing the thermometer in the flask usually results in a time delay in measuring the temperature of the air inside the flask. The flask should be fully immersed in the water, to ensure all the air in the flask is at the same temperature The temperature must be recorded as Absolute Temperature (in Kelvin) to find a relationship.

The pressure increases proportionally with the absolute temperature (i.e if you double the absolute temperature you will double the pressure provided the mass and volume remain constant). This can be expressed as:

###### The pressure law states that: *For a *__fixed mass of gas__ at __constant volume__ the pressure is proportional to the absolute temperature. *i.e. the pressure divided by the temperaturee stays constant, provided the volume does not change.*

*For a*

__fixed mass of gas__at__constant volume__the pressure is proportional to the absolute temperature.### Kinetic theory of Pressure law

If the absolute temperature of a gas increases, the speed of the molecules increases. The force and frequency of the impacts on the walls of the container increases, as this is the cause of pressure,then pressure increases.

**How Temperature is related to Pressure for a constant mass and volume of gas**.

Temperature ( o C) | 0 | 20 | 50 | 80 | 100 |
---|---|---|---|---|---|

Pressure (kPa) | 93 | 100 | 110 | 120 | 127 |

Use this to show a relationship! |

# Charles’ Law

This is about the variation of volume with temperature at constant pressure. The apparatus shown is used to find how the volume of air varies with temperature provided the pressure remains constant.

The pressure remains constant, since it is equal to the atmospheric pressure plus the small additional pressure due to the weight of the mercury bead on to of the trapped air. This is because the capillary tube is open at one end. The volume of air is measured on the scale and the water bath is used to vary the temperature. The absolute temperature must be used to find a relationship between pressure and volume.

It is found that the volume of the gas increases proportionally with the absolute temperature provided the pressure and mass remain constant. This can be expressed as:

###### Charles’ Law states that: *For a *__fixed mass of gas__ at __constant pressure__ the volumee is proportional to the absolute temperature. *i.e. the volume divided by the temperature stays constant, provided the pressuree does not change.*

*For a*

__fixed mass of gas__at__constant pressure__the volumee is proportional to the absolute temperature.* *Kinetic theory of Charles’ law

The pressure of a gas is caused by the molecules hitting the walls of the container. If the absolute temperature of the gas increases the speed of the molecules increases. This would result in more forceful and frequent collisions on the walls. However, to maintain the pressure then there must be no increase in the frequency and magnitude of the collisions, so the volume must increase.

**How Temperature is related to volume for a constant mass and pressure of gas**.

Temperature ( o C) | 0 | 20 | 40 | 60 | 80 | 100 |
---|---|---|---|---|---|---|

Length of air Column(cm) | 20 | 21.5 | 22.9 | 24.4 | 25.9 | 27.3 |

Proportional to volume | ||||||

Use these figures to show a relationship! |

# The General Gas Law

The three separate gas laws can be summarised by one equation, known as the General Gas Equation:

This is often written as:

Where p_{1}, V_{1} and T_{1} refer to one set of conditions of pressure volume and temperature, and p_{2}, V_{2} and T_{2} to another set of conditions for the same mass of the same gas.

An individual gas law can be found from this equation by covering up the variable which is kept constant (or cancelling out the variable as it remains constant).

Complete the three graphs above and for two of them try to work out the equation for the straight line, i.e. what is *y = mx + c*

# Pascal

The unit of pressure is the Pascal. I Pa is 1 Nm^{-2}. You must remember you will not measure zero pressure as we have an atmosphere. I atmosphere is the pressure exerted due to our atmosphere and is approximately equal to 1 x10^{5} Pa. This is equivalent to a weight of 10^{5 }N acting on a square of area 1m^{2}. At ground level this is approximately the mass of 10^{4 }kg on a square metre which equates to about 10 Fiat 500 in 1m^{2}.

# Questions

- A mass of gas at a pressure of 20kPa has a volume of 3m
^{3}. What will be the volume if the pressure is doubled but the temperature remains constant? - The volume of mass of a gas is reduced from 5m
^{3}to 2m^{3}. If the pressure was initially 40 Pa, what will be the new pressure if the temperature remains constant? - The pressure of a fixed volume of gas at 300 K is increased from 5 Pa to 10 Pa, what will the new temperature be?
- If pressure of a fixed volume of gas at 200 K is 50 Pa. What would be the pressure if the temperature is increased to 300 K?
- The temperature of 6 m
^{3}of gas is increased from 300 K to 400 K. What will be the new volume of the gas if the pressure remains constant? - The volume of a gas is increased from 10 m
^{3}to 20 m^{3}at constant pressure. Calculate the new temperature if the initial temperature was 300 K. - A mass of gas has a volume of 5 m
^{3}, a pressure of 20 Pa and a temperature of 300 K. What will be the new pressure if the volume is changed to 4m^{3}and the temperature to 400 K?

#### Answers

- 1.5 m
^{3}, - 100 Pa
- 600 K
- 75 Pa
- 8 m
^{3} - 600 K
- 33 Pa