in today's video we're going to look at how the internal energy of an object relates to its temperature using the concept of specific heat capacity now the first thing we need to do is take a look at a few terms internal energy is the total energy that's stored by the particles making up a substance or system and we often talk about it as if it's made up of two parts the potential energy stores and the kinetic energy stools the potential energy stores are things like gravitational and elastic potential but they're not really related to temperature so we can pretty much ignore them in this video on the other hand kinetic energy is the movement energy of the particles and this is the one that's important whenever you heat up a substance it transfers energy to the kinetic energy store of all the particles and so increases their internal energy we measure this as an increase in temperature because temperature is just a measure of the average internal energy of a substance so the more internal energy that a substance has the higher its temperature will be however some materials require a lot more energy to increase their temperature than others for example water requires four thousand two hundred joules of energy to warm one kilo a bit by one degree celsius whereas one kilo of mercury can be heated by one degree celsius with only 139 joules of energy we call these numbers the specific heat capacity which is the amount of energy needed to raise the temperature of one kilo of a substance by one degree celsius it can also be thought of as the amount of energy released as that substance cools so each time our kilo of water cools by one degree celsius it will give out 4200 joules of energy to the surroundings we can put this idea into an equation where the change in internal energy is equal to the mass times the specific heat capacity for that particular substance times the change in temperature where the triangle's meaning change and the zero the line through it being a theta sign which here means temperature to see how this works let's try a question find the final temperature of 800 grams of water at an initial temperature of 20 degrees celsius after 20 kilojoules of energy has been transferred to it the specific heat capacity of water is 4 200 joules per kilo per degree well in order to find the final temperature what we're really looking for is the change in temperature so to get that term by itself we need to divide both sides by mse giving us energy divided by mass times specific heat capacity equals change in temperature next we make sure all of our units are correct so change 800 grams to 0.8 kilos and change 20 kilojoules to 20 000 joules and then plug these values into the equation so overall we get a temperature change of 5.95 degrees and if we add that onto our original 20 degrees the final temperature would be 25.95 degrees or 26.0 degrees if we round it to three significant figures which we generally should one thing to point out here is that in real life the temperature probably wouldn't actually increase this much because some of the energy would be lost the surroundings mostly in the form of heat so if you're going to do this experiment in a classroom you'd want to make sure they used a lid and then you insulated it well anyway that's everything for this video so if you liked it then do give it a like and subscribe and we'll see you soon