00:01
Here we're going to look at a practical use for energy conservation.
00:07
So you can think about electrical devices in your home, turning electrical energy into other forms of energy.
00:23
Okay, so that is one way to think about them.
00:28
And one of the things that electrical energy is used for is to heat up ovens, to heat up water, to make toast, etc.
00:41
And here we're going to assume that there's a heating element.
00:45
All right, so we'll just simplify this, but it works kind of a similar way inside of an oven, but we're going to heat up a batch of water and run current through a heating element, which is nothing more than a resistor.
01:12
Okay, so there's a certain amount of energy that's coming from the current through the element, and we are converting electrical energy, in this particular case, into a thermal energy in water.
01:34
Now, we often write that thermal energy transfer.
01:40
Okay, so it's really a transfer, as q stands for heat or thermal energy transfer or change is, equal to if it's an object such as a chunk of metal, or if it is a mass of water, it does not undergo a phase change.
02:14
That q is equal to the mass of the system times if its specific heat capacity, usually at constant volume, if it's a liquid or solid, times the temperature change.
02:34
Now usually when we're talking about electrical energy, what we usually think about is electrical power is equal to the rate at which energy is transferred, and it's simply equal to the product of the current into the heating element times the voltage of the source.
03:18
So somewhere out here is a voltage source that's driving that current.
03:23
Most households, it's 220 volts or 110 volts.
03:29
For high power, things like the water heater or a furnace, it may be the 220 volts, whereas most things in the house are 110 volts.
03:43
So one of the practical applications we can do is we can determine the electrical current needed to heat up a water heater.
03:59
So that is our goal.
04:07
And by doing so, we'll figure out some things about the heating element.
04:21
Needed to heat up the water heater to, i don't know, to a safe temperature.
04:36
So here we'll outline some more details in the equations.
04:40
So first thing to do is specify the mass of water and the temperature change that you would like.
04:58
So most many, many mortar heaters are about 50 gallons, and that means that the volume is 190 liters.
05:12
And the density of water is one kilogram per liter.
05:20
So the mass of the water is density times volume or 190 kilograms.
05:27
That's a couple hundred pounds, over 400 pounds.
05:33
Typical temperature change, we want to go from 20 degrees centigrade up to 45 degrees centigrade.
05:47
And the specific heat of water at root temperature for a liquid, there will be no phase change.
05:55
We don't want to boil the water.
05:57
That would be very unsafe.
06:00
4 ,190 joules per kilogram, and sometimes it's in degrees centigrade or kelvin degrees or temperature change in kelvin.
06:12
And those are roughly the same, so we don't have to worry about changing temperature scales.
06:20
And the reason why they're the same is because we're looking at a temperature difference.
06:25
Not an absolute temperature.
06:29
So q is going to be in joules, and it's simply 190 times 4 ,190 times 25...