if you have a block of ice and Supply heat to it its temperature will increase the particles vibrate faster which means they're gaining kinetic energy however once it reaches the melting point of 0° C its temperature will remain constant until it's all melted only then will its temperature start increasing again the same thing happens when it reaches 100° and it turns into a gas but why the constant temperature after all energy is still going into the ice but during a change of state the particles don't gain kinetic energy but rather potential energy an increase in temperature means we must have an increase in kinetic energy of the particles while a change in state when heating anyway must mean an increase in potential energy during a change of state the temperature stays constant so we can't use the specific heat capacity equation instead we use the slh equation specific lent heat slh of a substance tells you how much energy is needed to change the state of 1 kilogram of it you know all of this from GCSE to be honest but the questions you can get can be fairly complicated at a level for example you might get two substances at different temperatures touching and they reach a common temperature in that case you equate the shc equations for both but replace Delta t with T minus T1 for the colder substance or object and T2 minus t for the hotter one then expand multiply out and rearrange to find the common temperature T if it's an ice cube melting in a drink for example you must add on the shc equation while it's ice and the slh equation there are many variations on these questions so just remember you equate the total energy gained by one object to the total energy lost by the other the Celsius scale is not an absolute scale that is it doesn't start at zero we know that the higher the temperature the higher the kinetic energy so we must have a scale that starts at zero when particles have in theory zero kinetic energy that's the Kelvin scale same increments as Celsius just shifted by 273 minus 273° C is 0 Kelvin this is absolute zero to convert degre Celsius to Kelvin just add 273 particles can be cooled to almost absolute zero but even if you don't have the kit to do this we can still cool a gas and measure the change in pressure at a constant volume or change the volume at a constant pressure plotting pressure or volume against temperature in degrees celsi we end up with a straight line extrapolating this to where it meets the x-axis a pressure of zero is absolute zero doing this by hand isn't very accurate so it's better to do this algebraically find the gradient then pick a point y1 X1 and then we just say y = mx plus C so that means that y1 mx1 = C and so therefore that's also equal to Y2 MX2 and you're looking for X2 when Y2 equal zero a pressure or volume of zero you must always use Kelvin when dealing with calculations involving temperature The Only Exception is the shc equation because that's a change in temperature a change in degrees celsus is the same as a change in kelvin this is Bo's law pressure is inversely proportional to volume at a constant temperature so P1 V1 equal p E2 V2 we call this an isothermal change ISO means same Charles's Law is this volume and temperature are proportional at a constant pressure so V1 / t1al V2 over T2 the pressure law also known as the gayc law pressure is proportional to temperature at a constant volume combining these three laws we can say that PV is proportional to T to turn this into an equation we need a constant that's big n * K where Big N is the number of gas particles or molecules and K is the botsman constant as big n is huge and K is Tiny we can swap them out for little n thus moles and R the molar gas constant or we might just say gas constant which is 8.31 much nicer numbers to deal with if only two out of PV and T are being changed we just use one of the above laws if all three are being changed and there's no molecules in or out so n or n stays constant then P1 V1 over T1 equal p2v2 over T2 we explain gas pressure with the kinetic theory of particles but our model only works perfectly with a theoretical ideal gas some real gases Come Close like ironically named perfect gases we must make five assumptions for an ideal gas so we can then use our laws it's the acronym raved R is for random particles move randomly we know this from browni and Motion demonstrated by the fact that if you put smoke particles under a microscope you can see them moving randomly due to air particles colliding with them A is for attraction as in there is no attraction between the particles of the gas V for volume the volume of the particles is negligible compared to the volume of the container e for elastic all collisions are elastic and D is for duration the duration of every Collision is negligible compared to the time between collisions to derive the kinetic theory equation we imagine a cube box of sides LX l y and LZ a molecule inside collides with one of the sight the area l y * LZ and it bounces off its change in momentum isus 2 mu but we can drop the minus we know that Force equals change in momentum over time but it's not exerting this force all the time so we use the time it takes between these collisions it takes two lots of distance divided by speed so 2 LX / U therefore force is equal to 2 muu over 2 LX / U which gives us mu ^2 over LX pressure is force divided by area so dividing by l y LZ we end up with P = mu ^2 over all three length and so that's the same as Mu ^2 over volume as any molecule can travel in three dimensions we say that u^2 is equal to a thir crms squ crms is the root mean Square speed this is essentially a usable average speed of the particles in a gas we know that in reality the average velocity is zero as the particles travel in all directions equally when averaged to calculate urms that's just the RMS value in one direction we add up their squares divide by the number of molecules then square root and so then C is a combination of U V and W the velocities in all three directions multiplying this equation by the number of molecules Big N gives us the pressure of the whole gas rearranging we can see that PV is equal to a thir nmc RMS s remember m is the mass of one molecule not the mass of the gas however big n * m does give us the total mass of the gas so that's why we can replace NM over V with the density of the gas so p is equal to A3 Row c^ 2 when doing calculations don't bother writing the RMS keep things simple as PV is also equal to nkt we find that mc^2 = 3 KT half this and we have kinetic energy half mc^ 2 C basically being the same as V so the kinetic energy of one molecule in a gas is equal to 3 KT that means if you know the temperature of a gas you can know the energy of one molecule multiply by Big N of course and you have the total kinetic energy of the gas notice there is no mass in the equation that means that no matter what particles you have in a gas say it's air it has nitrogen oxygen carbon dioxide molecules they all have the same kinetic energy because they're the same temperature however as they do have different masses they will have different speeds of course you saw what a PV graph looks like for Bo's law earlier we can draw an arrow to show whether the gas is being compressed or expanding at a constant temperature we can draw what happens if a gas is compressed at a constant pressure only volume decreases the area under any line on this graph equals work done Newtons per met squ Time by met cubed gives NM Newtons time meter that's yours work done if a gas is being compressed we say that work is being done on the gas if it's expanding we say the gas is doing work if the pressure is constant we can say that the work done by or on the gas is equal to P Delta V if you have a straight line going down that's a decrease in pressure at a constant volume so no work is being done whenever you supply heat to a gas it can cause its temperature and therefore its internal energy to rise or it can cause the gas to expand and do work in most cases it does a combination of both the first law of thermodynamics is therefore simple Q equals Delta U or sometimes just U plus W heat into the gas equals change in internal energy plus work done in expanding seems simple but using the equation can be tricky however firstly you need to deduce which of these are positive negative or zero Q is positive if heat goes in negative if heat leaves if it's a closed system and no heat enters or leaves then this is an adiabatic change so we can say Q is zero so that means U is equal to minus w we can also say that P1 V1 gamma equals p2v2 gamma where gamma is the a diabatic constant U is positive if the temperature of the gas increases if it gets hotter it's negative if the temperature decreases U is zero if the temperature doesn't change an isothermal change if that's the case we can say Q equal W finally W is positive if the gas expands the gas is doing work W is negative if the gas is being compressed work is done on the gas instead if pressure is constant we can replace W with P Delta v w is zero if the gas stays at a constant volume so that means Q equals U then all you have to do is pop in your numbers to find one of these that will be unknown leave a like if you found this helpful I've also put these into videos that cover whole papers click on the card for your board if it's there or go to my channel for more including International boards