00:01
We're taking a look at a piston system where we initially have 10 .0 liters of a gas, and we're going to wind up moving that piston up to a total volume of 18 .5 liters.
00:18
Now, inside that piston, we have a compartment that has 0 .2 .00 moles of the gas at 27 degrees celsius or 300 .15.
00:31
Kelvin.
00:33
And this expansion, when we go ahead and we go from 10 to 18 .5 liters, is going to happen isothermally.
00:39
The temperature is not going to change.
00:43
So the first thing we want to think about, if we want to take a look at entropy here, is what do we think is going to happen to the sign of delta s? does the entropy go up or down in this process? and so what we're doing here is we're isothermally increasing the volume, that gives the molecules more freedom because the volume is greater.
01:12
And if we give the molecules more freedom to move around, that creates more microstates.
01:21
And if we have more microstates, we have more entropy.
01:27
So we should expect the entropy to go up.
01:33
Now let's actually do some math and see if that's going to wind up being true.
01:39
And we can use the relationship that the change in entropy of the system is going to be equal to nr times the natural log of the final volume over the initial volume...