00:01
In this problem, you have 10 moles of a monotomic ideal gas that's taken from point a to point p on this route, and it asks some questions.
00:15
First off, it wants to know the temperature at a and temperature at b, that's part a.
00:20
So we can just use the ideal gas law.
00:27
So there it is for ta, solving for ta.
00:32
And everything we have can be read off of the diagram.
00:38
Remember, though, it's in kilopascal.
00:40
So you're going to have to convert.
00:41
Just put a 10 to the 3 in there.
00:43
P .a .va over nr.
00:47
Simple enough there.
00:48
So 10 times 10 to the 3.
00:52
Pascal.
00:55
Oh, this is, let me mark this.
00:57
1, 2, 3, 4, 5, 6.
01:02
So it's one cubic meter, n is 10 moles, and r is 8 .314 joules mole kel.
01:23
And this works out if you keep it to three digits, 1 .20 times 10 to the second kelp.
01:37
You write it in scientific notation because if you write 120, is that two digits, or is it three? significant digits.
01:45
This way makes it explicit that it's three.
01:49
Okay.
01:51
So tb is the same exact thing, just with a replaced by b, pb, b, b, and out.
02:01
Now you can put you in the values here, the six and so on, but really, don't even have to do that.
02:13
Pa, 6 times va, because 6 compared to 1, over nr, 6pa, p .a.
02:28
Over n .r.
02:29
Which is just 6t .a.
02:32
But if you're not comfortable doing that, just plug in, put in the values, and you'll get the same answer.
02:38
You may round, you know, to three digits there, you might have, i think you might have a 1, 7 .21 or 2 -2 or something.
02:46
Insignificant difference.
02:48
So this is 7 .20 times 10 to the second.
02:52
Kelvin.
03:02
So that's the temperature at a and b.
03:07
Now, part b wants to know the work done as you go from a to b.
03:15
The work done by the gas is the area under the curve.
03:28
So that's everything.
03:30
So all this, all this filled in.
03:34
So let me mark that.
03:37
Let me put the delimit this.
03:40
Now, how you break this up is a matter of choice.
03:42
You can break it up into many smaller rectangles and one big one in here.
03:49
That's just a matter of choice.
03:51
I'm going to break it up so you've got this long bottom rectangle.
03:55
So this here is what i'm going to call area one.
04:02
And then you have, here's area two, area three, and area four.
04:16
So this way you have two triangles, two triangles.
04:20
Two triangles.
04:21
And two rectangles to deal with.
04:27
So, writing that out, and you actually already may see that two and four are exactly the same, but i'll write them out of separate things, just to make it clear.
04:36
All right, so the area of 1, 10, kilopascal times 5 meters cubed.
04:47
So 10 times 10 to the 3, 5 cubic meters, plus now 2, 1ā2, 1ā2 .1ā2 .1 .5 .5.
04:58
Cubic meter height is 40 minus 10 so 30 10 to 3 pascal oh i lost my units here let me put my units in okay so that's the area 2 now we have a rectangle for 3 which is it's height if you like whatever how you want to call it 30 kilo pascal and it's width it's one cubic meter and the area four is the same as the area two, one half, one cubic meter, 30 times 10 to 3 pascal.
06:02
What you always want to do if you're doing this is obviously break it up into simple figures.
06:10
Don't do anything fancy.
06:13
And this works out to be 1 .10 times 10 to the 5th pascal.
06:22
Or not pascal, jewel.
06:25
So it's a work.
06:30
So that's the work.
06:33
Here you under the curve.
06:36
Now, part c wants to know how to change internal energy.
06:41
You might say, wait a second.
06:42
I got the work, but if you remember the first law, you might say, i need the heat.
06:48
How do i, the heat, though, is part d.
06:50
How do you do this? well, let me try to draw this as best i can here.
07:06
This is an isotherm for tb...