There's no change in entropy at all. Okay, so, the spontaneity and entropy

then, the feature I'd like you to notice about this system is that the spontaneous

flow of energy as heat from a body at a higher temperature to a body at a lower

temperature is governed by the condition, dS is greater than zero.

The heat stops flowing when they're at the same temperature.

And dS becomes zero thereafter. So, in an isolated system, the energy

remains constant. So any spontaneous process must be due to

an increase in the entropy. Unlike energy, entropy is not conserved.

So that's a key feature of entropy. It increases whenever a spontaneous

process takes place. And the entropy of an isolated system

will continue to increase until the entire system is in equilibrium.

And at that point the entropy remains constant.

At that point it will have its maximal entropy.

Continues increasing until it can't increase even more because it's at

equilibrium. So we say then that dS is greater than 0

for a spontaneous process in an isolated system.

And the sorts of things that can happen at equilibrium are reversible processes.

And for those, dS is equal to 0. So a way to think about this is that in

an isolated system, if you just start it out of equilibrium.

That was when I brought my two gases into contact with each other, at different

temperatures for instance, that spontaneous processes will occur.

So this is a plot of entropy against time.

So over time spontaneity, spontaneity, things are happening, things are

happening, entropy is increasing, increasing, increasing.

And finally, I hit a maximum value of S, the point at which the system is at

equilibrium. And at that stage the entropy does not

change any longer, dS becomes zero. So what about a general situation, a

non-isolated system? So isolated systems are convenient to

think about, but we're often interested in systems that can exchange heat, work,

what have you, with the surroundings. Well, in that case the change in entropy

comes from two sources. So there's the entropy produced just by

an irreversible process. So all these spontaneous irreversible

processes that are taking place, that's creating entropy.

And then, there's entropy because of heat exchanged.

So remember the definition of entropy would be the reversible heat change,

divided by the temperature, that defines dS.

So that's an exchange between the system and the surroundings that becomes

possible once it's no longer an isolated system.

And so we could write that as dS equals dS produced.

So that is always non-negative and associated with spontaneous processes

plus dS exchanged. And that can be positive, or negative, or

zero. It depends on the sign of the heat

transfer which way that might go. So, could also write dS produced over

delta q over T. So, for the reversible process, D S, I've

got a system at equilibrium. So it won't create any produced entropy,

spontaneous entropy. It can, exchange heat with the

surroundings through a reversible process.

Del q reversible over T that's, defines dS under reversible conditions.

Under irreversible conditions, I've got some entropy that comes from the

spontaneous process, plus an irreversible heat exchange with surroundings, delta q

irreversible over T. Because this quantity is always greater

than zero, that means that the net dS is greater than the irreversible heat

exchange with the surroundings divided by T.