00:01
Okay, so this question asks us to calculate the temperature between the joints or the point where a brass rod and a copper road are joined together.
00:13
All right.
00:13
And we told that in this question that we have the brass rod fixed inside boiling water.
00:19
And then we have the copper road, one of its end, also fixed in ice and water mixture.
00:26
All right.
00:26
So let me draw this diagram to represent the situation that was.
00:30
We've been asked to solve.
00:32
All right.
00:33
So this is my car.
00:35
Let's see my bull containing boiling water.
00:39
All right.
00:39
And then inside it's a brush rod.
00:43
All right.
00:44
And then let's see this is my copper word.
00:48
All right.
00:49
Which is also fixed inside.
00:51
Ice and water mixture.
00:55
Ice and water mixture.
00:58
All right.
00:59
So this is it.
01:01
Ice and water mixture.
01:03
All right.
01:03
Forgive my diagram.
01:05
Okay, all right.
01:06
So we told you that the brass has a length of 0 .2 ,000 meters, and then the length of the copper.
01:20
0 .8 meters.
01:25
All right.
01:25
Now, we want to determine the temperature, the common temperature between the joints where they are joined together.
01:31
But it's the point where we want to determine their temperatures.
01:34
All right.
01:34
Now, we need to understand that heat always flows from a hotter region to a cold region.
01:41
All right.
01:42
And we know that the brush flow, which is fixing a hotter water, will have heat flowing through it to the cold area inside where we can locate our copper.
01:52
All right.
01:54
So in this situation, we're going to talk about heat current.
01:57
All right.
01:57
Now, the equation talking about heat current is given as the heat current.
02:02
A is giving us the thermal conductivity times the area which will bracket a change in temperature minus the hot one minus the cold one divided by the length of the rod that we are considering.
02:18
Lent of the road that we are considering.
02:21
Now in this question since we're talking about two roads, since we're talking about two roads, we're going to change up this equation a bit to suit the situation that we are studying.
02:33
All right.
02:34
Now, since there is a common temperature between the joints where this road are set up, then we need to change our equation to look like this.
02:41
K, let me say k subscript b, that stands for brass, times the area to bracket t, subscript h minus.
02:51
Now, the common temperature we're going to represent with t.
02:54
All right, divided by the length, the brus, l, subscript b.
02:58
And all of this is equal to k subscript c times a.
03:03
Into bracket t -h, oh, sorry, forgive me, to bracket t -minus t -c.
03:11
Now, t -m -t -c, because the t -e will have a higher temperature than the temperature of the cold area, and all of this divided by the length of the copper.
03:22
All right.
03:24
Okay.
03:25
Now, we need to also understand this, that the joints where we have their temperatures, the same, what it means is that the heat current at a point in both roads are the same.
03:34
So we can straight away and equate these equations.
03:38
We need to understand that.
03:40
All right.
03:41
So we have our length of the road already given.
03:46
Okay, i've already written that...