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.

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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.

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.

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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.

We wanted to take that model one step further.

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This just links to the front.

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.