5.17 use the relationship between pressure and volume of a fixed mass of gas at constant temperature

P1 x V1 = P2 x V2

NOTE: this is sometimes written as P1 x V1 = constant

For example: A gas at a pressure of 250 kilopascals is compressed from a volume of 300cm3 down to a volume of 175cm3. The temperature of the gas does not change. Find the new pressure of the gas, in kilopascals.

Step 1: rearrange the equation to isolate one unknown

In this instance, we know P1, V1 and V2, and we are looking for P2. Therefore...

P2 = (P1 x V1) / V2

Step 2: substitute the known to find the unknown...

P2 = (250 x 300) / 175

P2 = 429 kPa (to 3 significant figures)

Example credit: CGP

5.16 use the relationship between pressure and kelvin temperature of a fixed mass of gas at constant volume

P1 / T1 = P2 / T1

Example: A container has a volume of 30 litres. It is filled with a gas at a pressure of 100 kPa and a temperature of 290 K. Find the new pressure (in kPa) if the temperature is increased to 315 K.

Step 1: rearrange the equation to isolate the unknown

The old pressure is P1
The old temperature is T1
The new pressure is P2 (this is what we are finding)
The new temperature is T2

if P1/T1=P2/T2 and we are looking for P2, we must rearrange the equation to...

P2 = (P1/T1) x T2

Step 2: substitute the known into the equation

P2 = (100 / 290) x 315

 = 109 kPa

NOTE: as we are asked to leave the new pressure in kPa, we do not need to convert it, if asked to leave the answer in Pa (and you have it in kPa) just multiply it by 100

Example credit: CGP

5.15 describe the qualitative relationship between pressure and Kelvin temperature for a gas in a sealed container

In a sealed container, temperature (in K) and pressure are proportional. This is because the higher the temperature the faster the molecules move the more pressure is exerted onto the walls of the sealed container. If you double the temperature, you double the kinetic energy (5.14), this will double the pressure.

5.14 understand that the Kelvin temperature of the gas is proportional to the average kinetic energy of its molecules

Temperature (in Kelvin) and kinetic energy are proportional. In other words, if you double the temperature, you will double the average kinetic energy of the particles. This is because as you increase temperature, the particles gain more kinetic energy.

5.13 understand that an increase in temperature of the gas is proportional to the average kinetic energy of its molecules

An increase in temperature means the particles will have more energy. In a gas, this means the particles will travel further (in a solid, the particles will break the intermolecular forces and become a liquid, in a liquid they will gain speed to become a gas).

5.12 describe the Kelvin scale of temperature and be able to convert between Kelvin and Celsius scales

Absolute 0, -273ºC, is the start of the Kelvin temperature scale (basically, 0K is -273ºC). The two temperature scales (ºC and K) have the same temperature change (e.g. a change of 12ºC is also a change of 12K) which is handy as it means conversion is super simple.

In order to convert from K to ºC all you need to do is -273 (and change the unit from K to ºC). Alternatively, to convert from ºC to K just ass 273. For example..


0K = -273ºC
0ºC = 273K
100ºC = 373K

NOTE: there is a little more information on Kelvin and absolute 0 (-273ºC) in post 5.11

5.11 understand why there is an absolute zero of temperature which is -273ºC

The coldest something can get is -273ºC (0K), this is because atoms have as little energy as they can possible have at this temperature (more heat = more energy, less heat = less energy). This temperature is known as absolute 0.

NOTE: to convert from ºC to K, just add 273. Alternatively, to convert from K to ºC just take away 273

NOTE NOTE: there is no º symbol when talking about degrees Kelvin, it is just a K

5.10 understand that molecules in a gas have a random motion and that they exert a force and hence a pressure on the walls of a container

Particle theory suggests that gas molecules has a random motion. When gas molecules collide with something (could be anything as they move in a random motion) they exert a force. If the gas is present in a sealed container they will exert an outward force should they hit the walls of the container.

NOTE: The pressure exerted is not the same for every gas/molecule, it will depend on how fast the particles are going and how often (as they will have more/less kinetic energy. The overall pressure felt on the object will depend on how fast the molecules are going and how often gas particles collide with its walls (more collisions = more force).

5.9 understand the significance of Brownian motion, as supporting evidence for particle theory

Brownian motion states that particles move in a random unpredicted motion (like they dont all more from north to south, or from up to down, they move wherever). Particle theory states that gases consist of particles that are constantly moving in a random direction.

These two theories support each other as particle theory claims that particles are constantly moving in a random motion, and Brownian motion claims that particles move in a random motion.

NOTE: Both of these theories can help explain post 5.5