00:01
Here i'll look at a situation in which conservation of energy applies.
00:07
Simply thermodynamics, of course, conservation of energy always takes place.
00:12
But if you have an isolated thermal system, you can do some more detail calculations with that system.
00:20
So we're assuming that you have two objects that are isolated from the rest of the universe.
00:26
One is at a high temperature and one is at a low temperature.
00:30
The zeroth law of thermodynamics says that they will come to equilibrium.
00:41
So the temperature will change in both of the objects so that the final temperature is equal or the same for both of the objects.
01:01
And how conservation of energy applies, conservation of energy applies in the sense that any heat that gets transferred out of the hot object goes into the heat flow into the colder object.
01:28
So they exchange energy.
01:31
And we now know that this is due to collisions between particles and the two objects.
01:36
Even if they're solid, they are conducting energy from one to the other.
01:42
So as an example of this, we'll take a fairly complicated example, but we have a styrofoam cup, so that is what's doing the isolation.
01:56
We can pretend it's not open to the environment that maybe it's got a lid on it.
02:03
And inside the cup, we have some soda.
02:07
I'll make it blue.
02:08
No, we'll make it green.
02:10
Yeah.
02:11
So we have some soda that's initially at room temperature.
02:21
I believe that's 20 degrees centigrade.
02:23
We'll assume that.
02:25
And the mass of the soda is 0 .25 kilograms.
02:35
Inside, we also have placed three small ice cubes that are just at freezing.
02:48
So there's some ice.
02:50
And the initial temperature of the ice is 0 degree centigrade.
02:57
The mass of the ice is fairly small.
03:00
0 .018 kilograms.
03:05
And we would like to know what is the final temperature that the soda arrives at final temperature after it's cooled off by the ice.
03:17
And but we have to realize this is exactly what the situation above is meant to address.
03:24
Is that the let's see, the hot stuff is the soda.
03:29
So the cue out of the soda has to equal the cue into the ice.
03:40
And the final temperature is going to be the same for the ice and soda.
03:51
So that is the zero with law coming into play.
03:55
So here's some things that we have to keep in mind, is that we need an expression for q.
04:01
And there are two expressions for q.
04:04
The first one is q is equal to m times the specific heat capacity times delta t.
04:11
This occurs off of a phase transition, no phase change.
04:19
During a phase change, though, such as freezing or boiling, the q does not depend on temperature.
04:28
Phase changes happen at a constant temperature.
04:33
So the q can be written as either the mass, times the latent heat of fusion or mass times the latent heat of vaporization.
04:43
Fusion happens for melting and freezing, and vaporization happens for boiling or condensing.
05:01
So let's think about which of these apply to our soda and ice.
05:06
The soda hopefully is not going to go through face change.
05:10
So the qs out is simply going to look like the mass of the sauce.
05:15
Soda times the c of the soda, the specific heat capacity, times, and really what we need is absolute values around those.
05:29
And so the temperature change is going to look like the initial temperature minus the final is a positive quantity because that is our hot stuff, t initial greater than t final...