Volume

Let me try my best to draw this neatly.

Well, they also tell us that the volume is 405.

So let's think about it.

So if I had a little cube here in the volume under consideration, that's a little cube you consider that dv.

So how do we figure out the volume under a surface like this?

In units, what are the dimensions of the box?

And that seems pretty reasonable for our reality.

And that little cube has side length 2.

So dy, which is this. dy times dx, dx times dz.

And that's that the ratio between the volumes let me write this down that the ratio between the volume at state B and the volume at state A so the ratio of that volume to that volume is equal to, in our Carnot cycle, is equal to the ratio between the volume at state C.

So this is the surface defined by this function.

Now if I multiply this whole thing times dy,

That makes sense because surface area is a 2 dimensional measurement. We think about how many sq cm can we fit on the surface of the cylinder.

It will make our denominator 0.

You either multiply the length of the rectangle times the entire width.

We piled the carcasses and burned them.

But you put one there. Why?

And we go straight through the centimeter that distance right over there is 14 centimeters.

With that out of the way, let's just apply this radius being 7 centimeters to this formular right over here.

Let me draw it.

These are the same rectangles.

Uranium hexafluoride is a gas.

And then it's going to be times the spanning vector itself.

So what's the volume of this shell?

And that width is dx, so it's going to equal this times dx.

It's kind of a constant y.

But that's the intuition of what we're going to do.

Then he cuts out a little cube of side length 2 from one of the corners of the cube.

Well, we know that the surface area of each cube is going to be 6x squared, where x is the dimensions of that cube.

A cube with side x has length x, width x, and height x.

But I'm going to make it a little bit more complicated.

If I multiplied this area times a small dy, then all of a sudden I have a sliver of volume.

They're going to essentially turn into water and disappear into the solution.

So if we have this unit step function, this thing is going to zero out this entire integral before we get to c.

And that's taking the integral.

So for this cube, the surface area is going to be 6 times 2 squared.

length times x times 9.

That's, literally, the volume of the box.

So let me does this, it's going to be 8 cm times 8 pi cm. And thats equal to 64 pi. 8 times 8 is 64.

And the volume that he takes out is the volume of that little cube.

That half of the rhombus

So what would be the volume of that sliver?

So there must have been 1 mole of hydrogen to begin with.

The particles, on average, are going to be colliding with the wall less often, and the walls are going to have a larger area, as well.