00:01
A certain brand of freezer is advertised to use 730 kilowatts hours of energy per year.
00:06
Assuming the freezer operates five hours a day, how much power does it require while operating? if the freezer keeps its interior at minus five in a 20 -degree c room, what's the theoretical maximum? performance coefficient, what's the theoretical maximum? on advice that the freezer can make an hour starting with 20 degrees c.
00:22
Okay, so first part, i wrote down all of the givens ahead of time.
00:30
And so first we want to get the power required while operating, assuming it operates for five hours a day.
00:39
So power equals question mark.
00:42
So power in general is energy over time.
00:45
So let's see.
00:45
This is going to be part a.
00:49
And the energy is given by this first quantity is 730 kilowatt times hour, kilowatt hours.
00:58
And the time is this t run, so i'll go ahead and put that coefficient on the t just to make it clear.
01:05
So t run, and that's 1825 hours.
01:08
So if you take the ratio of 730 kilowatts times hours divided by 1825 hour, then you should get that the power is 400 watts, so 400 joules for second.
01:25
And for part b, the goal is to get k.
01:31
So k is equal to tc over th minus tc.
01:43
I forgot to write down the temperatures and the givens, but that's okay, i can just write them down here.
01:47
So t -cold is minus 5 degrees c, but of course you can't forget to use kelvin.
01:56
And then t -hot minus t -cold, that's just our delta t.
02:02
So that's just this minus, oh, never mind, that's not our delta t.
02:10
This t hot minus t cold is the difference between the two reservoirs.
02:14
That delta t i'll talk about later in the problem.
02:17
So this delta t is this t hot, which is 20 minus negative 5.
02:28
And so if you put that into a calculator, notice i didn't convert the numerator to calvins, and that's because temperature differences can, be equivalently done in calvins versus celsius.
02:43
So if you put that into a calculator, maybe i'll get what i got, which is 10 .7.
02:48
And now that i remember it, i will box that.
02:56
Okay, all boxed up.
02:59
So for part c, now we want to get to like a, maybe a more question you can actually picture asking.
03:08
So what is, how much ice can this freezer make? so for this, we kind of need three equations.
03:15
I kind of thought about it ahead of time and organized it this way.
03:19
One, we need to figure out how much heat is required to make ice.
03:23
So we want to use...