 Okay, so heat is the amount of energy you need to add to something to warm it up. But I would actually calculate precisely how much energy is required, how many joules of heat or energy you need to change the temperature of something by, say, 10 degrees. Well, the way you work that out is by using a number known as the specific heat capacity. It's written with a letter C and it's defined as the amount of energy you need to add or subtract to 1 kilogram of some material to change its temperature by 1 Kelvin. If you write that down as an equation, the amount of energy you need to add or subtract is written as delta E. That triangle is a capital Greek letter delta and that means the change in the energy. So it's the amount of energy you're adding or subtracting. Now that is equal to the mass of the object in kilograms times the specific heat capacity times the change in temperature. And once again we're using that big triangle of the capital Greek letter delta to indicate the change in temperature. So the change in energy of a system equals the mass times the specific heat capacity times the change in temperature. Okay, so let's do an example of this. Let's say you want to have a nice hot bath after coming home from a hard day at school. How much energy are you going to need to warm up the water for a bath? Now, okay, so we're going to need to work out the change in temperature, the mass of the bath, and the specific heat capacity. The specific heat capacity you would look up. So for water, specific capacity is roughly 4,186 joules per kilogram per Kelvin. So that's the specific heat capacity of water. Look it up. Now what's the change of temperature? Well, let's say the water is coming out of the pipes at, let's say it's a cambera and it's winter, maybe at 10 degrees C. And a nice hot bath would be about 38 degrees C. So we're going to change the temperature from 10 degrees centigrade to 38 degrees centigrade. So the change in temperature equals 28 degrees centigrade. Now that's in centigrade. We need it in Kelvin. But it turns out that the change in Kelvin is the same as a change in centigrade. Because if you remember, the temperature in Kelvin is just equal to the temperature in centigrade plus 273.15. So if you take two different temperatures and subtract them in centigrade, or two different temperatures and subtract them in Kelvin, this will cancel out and you'll get the same answer. So delta T is that. It's also the same value in Kelvin. Finally, we need to work out the mass. So what's the mass of water in a typical bath? Okay, so let's imagine our bath is, I don't know, 1 meter long, maybe 40 centimeters. It's 0.4 meters wide. And I don't know something like 30 centimeters deep the water, 0.3 meters. It's probably not an unreasonable size for a bath. And we'll approximate it as a cube of water. It's not really a rectangular prism of water. It's not really, of course, actual baths are curved, but that will get us fairly close to the right answer. So the volume is going to be roughly 0.4 times 0.3 times 1, which is equal to 0.12 cubic meters. That's the volume of water, but what we need up here is the mass of water. So the mass is just equal to the volume times the density, the ring-letter row. Density of water is by definition 1,000 kilograms per cubic meter. You can look that up again. So that equals 0.12 times 1,000 equals 120 kilograms. Is that plausible? Well, I mean, the water in a bath is pretty heavy. If you poured that much water into a bucket, it would be almost impossible to lift, but not totally impossible. That's probably about the same as the weight of a big person, so that sounds like a reasonably plausible number. Okay, so now how much energy do we need? Let's use that equation. So delta E equals the mass, which is 120 times the specific heat capacity, which is 4186 times the change in temperature, which is 28 Kelvin, which comes out as 14064960 joules, roughly speaking 14 million joules, 14 megajoules, which is a lot of energy. That's why running a hot bath will bump up your energy bill quite a lot.