Gas Laws

Pressure

Pressure is a measure of the amount of force over an area. In a gas the pressure comes from the collision of the moving particles with the sides of the container the gas is in. The more collisions per second the greater the pressure of the gas. As the particles collide with the wall they create a small outward pushing force on the wall. The overall effect of the billions of tiny collision is to create a net force at right angles to the wall.

Any change to the gas or the container that affect the number of collision will affect the pressure.

In this example the particles are moving about randomly and some will collide with each of the sides creating the force needed to produce the pressure.

When volume of the container is reduced, the particles have less room to move about. This increases the number of collision with the walls and increases the pressure.

Pressure is proportional to the volume of the container.

The relationship between the volume and the pressure is known as Boyle’s Law. Boyle’s Law assumes that the temperature (the speed of the particles) remains constant.

Adding more gas to a container will also increase the pressure, as there are more particles to collide with the walls. If the pressure is high enough the walls of the container can be force outwards. This is what happens when a type is pumped up using a bike pump.

Temperature

Temperature is a measure of the amount of kinetic energy of the particles in a material. The higher the temperature, the greater the speed of the particles. In a gas this results in the particles colliding with the wall more frequently and with greater force. These two effects results in a rise in pressure as the temperature of the gas increases.

Pressure is proportional to temperature for a fixed mass of gas: known as__ Charles’s Law__.

If the temperature of a container increases too much due to overheating the pressure will rupture the container and it can explode. This is why sealed containers of gas should not be placed near a heat source like a fire. If the container is not sealed then the extra pressure results in the gas escaping and so reduced the overall volume of the gas preventing the pressure from getting dangerously high. In systems that heat gases these are known as escape values.

Logically if temperature is a result of the movement of the particles, there must be a temperature at which the movement of the particles is zero. The point at which they stop moving is known as Absolute Zero (-273 °C). As it is impossible to go slower than zero, there is no temperature below -273 °C.

Kelvin Scale

There are several different scales for measuring temperature. In science in the UK the Celsius scale is most commonly used. It takes its zero point as the melting point of ice. The Celsius scales takes the boiling point of water as 100 degrees and divides the scale into 100 equal parts between these two reference points.

The Kelvin scales takes its zero point as Absolute Zero, each degree is the same size as a degree in the Celsius system. There are no negative values in the Kelvin scale as there are no temperatures below absolute zero.

The symbol of degrees Kelvin is °K

Converting between Kelvin to Celsius

 °C to °K add 273 °K to °C subtract 273

Examples

Freezing point of water 0°C add 273 gives 273 °K

Water boils at 373°K which is 373 -273 = 100°C

Body temperature is 37°C which is (37 + 273) 310°K

Any calculations to find pressures, volumes or temperatures of a gas must be done using the temperature values in Kelvins not Celsius.

Universal Gas Law

The changes that affect pressures and volumes of a gas are linked to temperature changes too, but if the temperature of a gas is kept constant then the changes to the pressure and the volume can be expressed in a simple relationship as follows;

Pressure x Volume before a change = Pressure x Volume after a change

P¹ x V¹ = P2_ x V_2 at a constant temperature.

Examples

1. If a gas has volume of 3 m3 at 1 x 10m3 Pascals _what will the new volume be if the pressure increases to 3 x 105 _Pascals?
 P1 x V1 = P2 x V2 so P2 = P1 x V1V2 = (1 x 105 x 3) 3 x 105 = 1m3
1. If a container has 0.1 m3 of air at a pressure of 4 x 105 Pascals _(_Pa) and the pressure drops to 3 x 105 Pa what is the new volume of the gas?

P1 x V1 = P2 x V2 so 4 x 105 x 0.1 = 3 x 105 x V2

 4 x 105 x 0.1 = 3 x 105 x V2 4 x 104 = 3 x 105x V2 V2 = 4 x 1043 x 105 = 0.13 m3
When a balloon is filled with air what causes the internal pressure on the surface of the balloon?
net force
Explanation: Inside the balloon are billions of air molecules, all of which are moving. As these collide with the surface of the balloon they push it outwards with a small force. The combined effect of these small forces produces a net force at right angles to the skin of the balloon. This net force spread over the area of the balloon’s surface creates the internal pressure.
Explain what happens to the pressure of a gas as its temperature increases.