 So we've learned about forces which are one way to figure out how things behave in a classical system And if you know that all the forces you can work out what's going to happen in the future. That can be quite complicated though Simple ways of working things out involved looking at conserved quantities And the first one we saw was momentum. Now momentum is always conserved. It only has one form The only disadvantage is it's a vector So it has three components It's got a magnitude and direction And so when you write down a conservation momentum what you're really writing down is three conservation laws The conservation momentum in the x-direction, the conservation in the y-direction and the conservation in the z-direction all in one hit A simpler quantity that only has a scalar quantity something like a charge and charge is always conserved But problems that require us to use the conservation of charge don't turn up that often except in more exotic situations So while being completely true and very important, it's not very useful There's mass. Mass is just a scalar But it's not always conserved. It's mostly conserved. That said Non-relativistic speeds and so forth when you're not worrying about nuclear reactions mass is effectively conserved So you can use things like conservation of pens or conservation of storm water for a lot of water goes into a drain You can figure out how fast the water has to be coming out the other end You can work out traffic flow and so forth using conservation of mass. So that's a good rule of thumb And we've also learned about conservation of energy. Now energy is important in lots of everyday situations It's a scaler. So that's very handy and it's always conserved, which is great The only problem is it comes in lots of forms and so to use it you have to learn all the different forms of energy and track How energy travels from one to another And in fact this tracking of how energy and learning how to use energy is one of the main things that enabled us to change our Technology over the last few hundred years from all the millions of years of fairly static technology beforehand Access to available energy is absolutely critical to our modern life It is a dominant force in international and domestic politics and you might ask the question if energy is conserved How can that possibly be and the answer is fairly simple energy has a lot of different forms And some of those are really easy to use and some of those are basically impossible to use So for the vast majority of human history the main energy source that we could access was the energy stored in our own muscles or If we're going to get the biology right more specifically I guess the bog of it was stored in the liver in the form of glycogen or in fat cells in the form of fat now How did that as you get there? Well, that's a long story Essentially it came from nuclear reactions in the sun into sunlight Light down in through the sky into plants plants converted into sugars the sugars are either eaten by animals or by us and then The animals were eaten by us and somehow all that got together into our glycogen and fat stores And we could run jump and adjust our environment to our hearts content and even of course once we use that energy the energy isn't gone It's just changed form So what's happened is that chemical potential energy in the chemicals in our body has turned into some kind of useful work and some waste heat It was actually the unbelievably important discovery that heat was a form of energy That allowed us as a species to go beyond the limits of what could be done with just the chemical energy Stored in our own muscles and the muscles of any animals that we domesticated Besides perhaps the occasional water wheel all energy that we were using was coming from us And this is a huge limitation even if we were using machines to try and use that energy And do that work as efficiently as possible So instead when we discovered that heat was a form of energy We learned not only that we could put work and create heat so we could say Bore out a cannon and make it hot in the process We also discovered how to do the reverse which is how to use a fire To make say a steam engine and create work and useful energy out of making things hot When we discovered we could burn things in some way and make them hot and then use that to do work That's what changed the world That's how we got from millions of years of very stable technology to suddenly the industrial revolution and things changing on an enormous scale So at a microscopic level heat energy is really just the kinetic energy of the particles moving around So if you have a gas of particles and they're all moving around at different velocities Then they each have different kinetic energy But on average you'll have a certain amount of energy Stored in the kinetic energy of that gas and that's the heat energy ultimately And the hotter something is then all these things are bouncing around and they'll have this bigger hotter distribution of energy They'll have more energy per particle on average So in the context of trying to get energy out of our muscles and to do useful things Then normally we think of the work as the important thing So this is stuff done by the force that our muscles produce And we think of the heat as a waste byproduct and indeed that's often the case So often when you're trying to use energy you end up producing some kind of low temperature heat as a result And if you produce high temperature heat like if you're building a fire in a steam engine You can use that to do work But if you have low temperature heat then you're basically that energy is not in a usable form anymore And there's this whole discipline of physics called thermodynamics where we talk about exactly what the limits are on trying to extract energy out of different sources of heat So when you talk about using energy you're really talking about transforming energy from one form to another form Well, sometimes from one form to multiple other forms of which you really only want one of them And that means that we always have to worry about the efficiency of that process Which is just the fraction of energy that you extracted into the form you wanted Divided by the total amount of energy that you used So in this case it would be the work divided by the chemical potential energy that we used