[MUSIC] So energy comes in units as well, and these are gonna be a pretty fundamental currency that we'll be talking about in this class, so we'll pay special attention to them. The fundamental unit of energy, an amount of energy, the unit that I find easiest to envision is the calorie. The calorie is the amount of energy that it takes to warm up 1 gram of water by 1 degree centigrade. So a gram of water is about a milliliter, so about a centimeter on each side, about the size of a plump raisin. If you make that 1 degree warmer, the amount of energy it took to do that is 1 calorie. You see calories on the dietary labels of food. And it's kind of a weird thing, dietary calories by convention mean kilocalories. A kilocalorie is 1,000 calories. So a factor of 1,000 there in your diet shouldn't throw you off too much, I hope. And then the energy unit that we will use most in this class, however, is joules and a joule is just 1 calorie is equal to 4.18 joules. So a joule is just a constant times the calorie its like inches and centimeters, their analogous, their the same dimension but they are different units. So we'll get some practice at slinging units around by trying to deconvolve this very curious unit that shows up on our electrical bills, a kilowatt hour. So a watt is a rate of energy flow. It's in units of joules per second. So if a joule is a quantity of energy, a watt is a rate of flow of that energy. So a kilowatt-hour means that we have a 1,000 watts of power flowing for a period of 1 hour. But we can simplify this considerably because there are time units in here twice. I'll show you what I mean. So we can simplify this down actually just to joules. So first we'll attack this kilowatt, kilowatt is equal to a 1,000 watts, so now we can cancel the kilowatts, and a watt is defined as 1 joule per second. Now, this is kind of a strange looking fraction because you have a fraction bar here on top and a fraction bar down there, so we can actually simplify this by writing second down here and getting rid of this bit. That's what this joules per second up on the top meant, is the second has to go down below. And then we've got hours and seconds. We can cancel those time units but only after we get them into the right units. So we'll go 60 seconds equals a minute. So the seconds go away. And then, 60 minutes equals an hour. The minutes cancels so now we just have hours and hours. Both cancel and we are left with the only unit remaining is joules, a quantity of energy. So when you get your electric bill this is the quantity of energy that you have consumed but they're these obtuse units, we can simplify them to the more straight forward units of joules. And the number comes out to be a big one. There are different ways that you can write this. Scientific notation. The way we normally write it with pencil and paper would be 3.6 times 10 to the 6th power. That would be sort of shorthand for this. 3.6 million written here in long notation. So, some of the answers in the exercises in the Coursera site have large numbers like this, and it's kind of a hard thing to type out. That many zeroes, you have to count how many there are. And it doesn't accept notation like this with a times 10 raised to an exponent. The way computers express scientific notation is like this. 3.6 E to the 6th means 3.6 times 10 to the 6th. Or another that this could be expressed that would also be valid, would be 36 E to the 5, because there's no decimal point here. Then it's 36 plus five 0s, like that. [MUSIC]
