00:01
In this example, we have a circular lake.
00:03
It has a radius r equals 1400 kilometers and it has a depth of d equals 10 meters.
00:20
Okay, the surface of the lake absorbs solar energy at a rate of power per surface area equals 200 watts per meter squared.
00:39
Okay, this lake is thermally insulated from its surroundings so it does not exchange any energy with the surroundings.
00:46
What we want to find is how much time is required to raise the temperature of the lake from an initial temperature of t initial equals four degrees celsius to a final temperature of t final equals 17 degrees celsius.
01:04
Okay, so the first thing we want to do is find the amount of heat required to do this.
01:12
Okay, so the amount of heat required to do this is equal to q equals the mass of the water times the specific heat capacity of water times the change in temperature.
01:29
Okay, so the mass of the water, we're going to need the density of water and then we're going to need to find the volume of the lake.
01:37
Okay, we're also going to need delta t.
01:39
Delta t is just t final minus t initial so that's just going to equal 17 minus 4, 13 degrees celsius.
01:47
Okay, and that's an increase in temperature.
01:50
Okay, the specific heat capacity for water equals 4 .187 times nothing times 10 to the nothing 4 .187 kilograms over no sorry kilojoules kilojoules over kilograms degrees celsius.
02:15
Okay, and the density of water, rho of water equals 1000 kilograms per meter cubed.
02:26
Okay, so first let's start by finding the mass of our water.
02:31
So, the mass of my water is going to equal the density of water times the volume of my water.
02:41
So, that's just the depth.
02:42
Depth times pi r squared.
02:49
Okay, we can picture this lake as a cylinder kind of with a height of 10 meters.
02:55
Okay, so the radius is 1400 kilometers so pi r squared.
03:02
Okay, what does this give me? okay, so this is quite a lot of water.
03:08
I get 6 .16 times 10 to the 16 kilograms of water.
03:19
Okay, kilograms of water...