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

5.8 describe the arrangement and motion of particles in solids, liquids and gases

NOTE: again, if you are unsure of these/need a little more guidance it may be an idea to check out my chemistry blog (this time post 1.1) as there is a little more information there just describing the formation of particles/changes in the conversion triangle etc.

image credit: oxnotes

5.7 understand the changes that occur when a solid melts to form a liquid, and when a liquid evaporates or build to form a gas

Solid to liquid - when a solid is heated, its particles gain more energy, this makes the particles vibrate more which weakens the forces that hold a solid together, this makes the solid expand. At a certain temperature, known as 'boiling point' (different for different substances), the particles have enough energy to break free from their positions.

Liquid to gas - when a liquid is heated it will evaporate/boil. When this happens, the particles gain more energy, this energy makes the particles move faster which weakens and breaks the bonds holding the liquid together. At a certain temperature (different for different substances), the particles have enough energy to break their bonds.

NOTE: if you are unsure of these or need a little more info to understand, it may be able to head to post 1.2 of my chemistry blog where there is a little more info on interconversions

5.6 know and use the relationship for pressure difference

pressure difference = height x density x gravitational constant


p = h x ρ x g

NOTE: You may have learnt the gravitational constant on earth to be approximately 9.8 (as did I) BUT it is rounded to 10 for iGCSE exams (it's on the formula sheet) so make sure to use 10 in exams not 9.8

For example...

The density of water is 1g/cm³. Find the pressure difference between the top and bottom of a 3m vertical column of water.

First, convert all units into the same (sorry, that didn't make much sense). Basically what im saying os ensure all measurements are in the same unit, like all distance is in m (or cm) and all mass is in kg (or g) etc. In this particular example, we need to convert 1g/cm³ into kg/m³ (alternatively, you could convert the 3m into cm, but for now lets stick with kg/m³). So...

1g/cm³ = 1000kg/cm³ and in this example we only have 1g/cm³ so no calculations regarding units have to take place :)

Next substitute all the facts we are given into the equation 'pressure difference = height x ρ x g

Pressure difference = 3 x 1000 x 10 = 30,000 Pa

NOTE: Pa (pascals) is equivalent to N/m² so don't be thrown of in an exam situation if the unit given is N/m² (it basically means pascals, the unit for pressure)

example credit: CGP

5.4 know and use the relationship between pressure, force and area:

pressure = force / area

p = F / A

NOTE: do not get confused with p (pressure) and  ρ (rowe, density)

5.5 understand that the pressure at a point in a gas or liquid which is at rest acts equally in all directions

Pressure is a measure of the force being applied to the surface of something. In gases and liquids (at rest) the pressure at any point acts equally in all directions. for example, if you fill a bag with water, then poke a hole at the bottom of the bag, water will 'squirt' out of the bag (obviously). However, if you put a hole near the top of the bag, the water will 'squirt' out with the same force. This is because the pressure of the water is the same at the top of the bag as it is in the  bottom of the bag.

5.2 know and use the relationship between density, mass and volume:

density = mass / volume

ρ = m / v


NOTE: do not get confused with p (pressure) and  ρ (rowe, density)

5.1 use the following units: degrees Celsius (oC), kelvin (K), joule (J), kilogram (kg), kilogram/metre3 (kg/m3), metre (m), metre2 (m2 ), metre3 (m3), metre/second (m/s), metre/second2 (m/s2 ), newton (N), pascal (Pa)

degrees Celsius, oC, measure of temperature
kelvin, K, measure of temperature
joule, J, measure of energy
kilogram, kg, measure of mass
kilogram/metre3, kg/m3, measure of density (interchangeable with g/cm3)
metre, m, measure of distance
metre2, m2 , measure of area
metre3, m3, measure of volume
metre/second, m/s,  measure of speed
metre/second2, m/s2,  measure of acceleration
newton, N, measure of force
pascal, Pa, unit of pressure

4.15 use the relationship between power, work done (energy transferred) and time taken:

Power = work done / time taken

P = W / t

For example...

A motor transfers 4.8kJ of useful energy in 2 minutes. Find it's power output...

As work done is the same as energy transferred, we know that 4.8kJ of work was done. Therefore...

4800 / (2 x 60) = 4.8 / 120 = 40 W

NOTE: remember to convert kJ to J and minutes into seconds.

4.14 describe power as the rate of transfer of energy or the rate of doing work

Power is the rate of energy transfer, or the rate of doing work, it is different to force and energy. The unit for power is watts (W), 1 watt = 1 joule of energy transferred per second. This means a watt is the same as a 'joule per second', they are interchangeable, watt is more commonly used just because few people may get confused with 'joule' and 'joule per second' (which are vert different things).

4.13 understand how conservation of energy produces a link between gravitational potential energy, kinetic energy and work

When something is falling, GPE is being converted into KE. This means that the further it goes, the faster it falls (well, until it reaches terminal velocity), as it is gaining more KE the further it has fallen. This equation may be useful to remember...

Kinetic energy gained = gravitational potential energy lost

4.12 know and use the relationship: kinetic energy = 1/2 x mass x speed2

0. 0. kinetic energy = 0.5 × mass × speed2 
      
   
   
   KE = 0.5 x m x v 2 
   

4.11 know and use the relationship: gravitational potential energy = mass x g x height

Gravitational energy = mass x g x height

GPE = m x g x h

NOTE: g stands for gravitational constant, which is around 9.8 on earth (rounded to 10 for exam purposes)

4.10 understand that work done is equal to energy transferred

Pretty self explanatory... work done is another way of saying energy transferred.

Basically, when a force is moves on an object, energy is transferred and work is done.

4.9 know and use the relationship between work, force and distance moved in the direction of the force:

Work done = force x distance moved


W = F x d


Example...

A tow truck drags a car 5m with a force of 340N, find the work done.

5 x 340 = 1700J

NOTE: Work done is measured in Joules, this is because it is the same as energy transferred (and energy is measured in Joules)

4.7 explain the role of convection in everyday phenomena

In everyday phenomena, convection can be useful as it will move hot air upwards. This can be useful when heating a room - hot, less dense, air by the radiator rises, its place is filled with cool, dense air, this heats, rises etc.

4.5 describe a variety of everyday and scientific devices and situations, explaining the fate pf the input energy in terms of the above relationship, including their representation by Sankey diagrams

Of course all things aim to be 100% efficient, but  thats virtually impossible. A Sankey diagram is a good way to visualise how much energy is wasted/useful (the more useful energy that goes out, the more efficient the object is). For example...

The useful energy output for a lightbulb is light energy, because thats what we want to come out. However, some of the electrical energy is transferred into heat energy. This is an example of a very inefficient lightbulb, only 10% of the energy input comes out as useful energy, the rest comes out as heat (wasted) energy.

NOTE: Inefficiency is the same for many everyday situation, e.g. a fire (for warmth) creates light; a pepper grinder creates sound (even though you just want it to move).

NOTE NOTE: In Sankey diagrams, the 'down' arrow (s) is the wasted energy, the 'straight' arrow(s) is the useful energy

4.4 know and use the relationship: efficiency = useful energy output / total energy input

Pretty self explanatory... efficiency = useful energy output / total energy input

4.3 understand that energy is conserved

Energy can never be 'lost' or 'used up', only every transferred. For example, when you turn a light on, electrical energy transfers to light energy (and a little heat energy).

4.2 describe energy transfers involving the following forms of energy: thermal (heat), light, electrical, sound, kinetic, chemical, nuclear and potential (elastic and gravitational)

This basically means what are the types of energy...

Electrical energy > whenever a current is flowing
Light energy > from the sun, light bulbs etc (when light is 'given off')
Sound energy > noise, e.g. when you should, or from a loudspeaker
Chemical energy > in foods , fuels, batteries etc
Kinetic energy > movement (everything moving has kinetic energy)
Nuclear energy > released nuclear reactions (and nothing else)
Thermal energy > this flows from hot objects to cold ones (also known as heat energy)
Gravitational Potential Energy (GPE) > anything that has the potential to fall has GPE. E.g. if you hold a tennis ball, it has GPE.
Elastic Potential Energy (EPE) > anything that can stretch has EPE. For example an electric band or a spring

NOTE: GPE, EPE and chemical energy are forms of stored energy, because the energy is not doing anything (unlike kinetic energy, for example), its just sort of there.

4.1 use the following units: kilogram (kg), joule (J), metre (m), metre/second (m/s), metre/second2 (m/s2), newton (N), second (s), watt (W).

kilogram, (kg), measure of mass
Joule,(J), measure of energy
Metre, (m), measure of distance
Metre/second, (m/s), measure of speed
Metre/second2, (m/s2), measure of acceleration
Newton, (N), measure of force
Second, (s), measure of time
Watt, (W), measure of power

3.32 relate the loudness of a sound to the amplitude of vibration

If there is a bigger amplitude, the sound will be louder, if there is a smaller amplitude, the sound will be quieter.

3.31 relate the pitch of a sound to the frequency of vibration of the source

The frequency is the complete number of vibrations per second. If the wave has a high frequency, the pitch is high (e.g a squeak), comparatively, if you have a low frequency (not very many oscillations per second), the pitch will be low (e.g a bear).

3.30 describe an experiment using an oscilloscope to determine the frequency of a sound wave

Method

- Plug a microphone into an oscilloscope
- Make a noise into the microphone (e.g. have someone sing a single note)
- Count the amount of oscillations per second (an oscillation is one complete wave, basically the wavelength)\

This is the frequency (as frequency is wavelength/time)

3.29 understand how an oscilloscope and microphone can be used to display a sound wave

A sound wave receiver (microphone, for example) picks up sound waves that are trade;;ing through the air. In order to display these waves (which is useful for measuring properties etc), you can plug the receiver into an oscilloscope (a decide which displays he microphone signal as a trace on a screen). The receiver will convert the sound waves to electrical signals. The appearance of the wave (basically what it looks like) can tell you whether the sound is loud or quiet, low or high pitched etc. You can also take measurements to calculate frequency etc (this is done by adjusting the display of the oscilloscope).

Reading the oscilloscope - the greater the amplitude of the wave, the more energy it carried. In sound, this means the greater the amplitude the louder the sound.