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### The Entropy of the Universe & the Surroundings

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• Intro 0:00
• Entropy of the Universe & the Surroundings 0:08
• Equation: ∆G = ∆H - T∆S
• Conditions of Constant Temperature & Pressure
• Reversible Process
• Spontaneous Process & the Entropy of the Universe
• Tips for Remembering Everything
• Verify Using Known Spontaneous Process

### Transcription: The Entropy of the Universe & the Surroundings

Hello and welcome back to www.educator.com and welcome back to Physical Chemistry.0000

Today, we are going to talk about the entropy of the universe and the surroundings.0004

Let us just jump right on in.0008

Let us start with the most fundamental equation that is important to chemists.0011

Let me go to blue today.0017

Let us start with δ G = δ H - T δ S.0024

Every property of this equation, the δ G, the δ H, the δ S, and T, in fact every property that we have been dealing with0036

in all the equations that we have dealt with, they are all properties of the system.0043

Unless they specifically say otherwise, the assumption is that they are always property of the system not the assumption but they are.0047

They are the properties of the system.0055

Basically, this is δ G of the system equals δ H of the system - T δ S of the system.0059

We will put it there because that is the general presumption.0072

under conditions of constant temperature and pressure which accounts for 99.9% of work that is done in the laboratory,0076

we know that if the δ G is less than 0 and that implies a spontaneous process.0094

That is the very definition of the spontaneous process, the δ G has to be less than 00110

that means that the equation as written will move in the forward direction from left to right.0115

δ G equal 0, this is the δ G of the system.0121

Under constant pressure, we also know under constant pressure we know that the δ H happens to equal0125

the heat of transferred in that process when the process is done under constant pressure.0139

The heat that flows to the surroundings is just the negative of the heat that goes into the system.0146

Heat has to come from somewhere.0164

If it goes to the surroundings, it is coming from the system, it is coming from the surrounding and is going to the system.0167

The heat that flows to the surroundings is just - Q that is equal to - δ H.0172

Because Q is δ H so- Q is - δ H that is the heat.0183

This is the δ H of the system, this is the heat that flows to the system.0187

This is the heat that flows to the surroundings.0193

If we suppose a reversible process the DS of the surroundings is equal to - DQ/ T.0195

- DQ of the surroundings which is this thing right here = - δ H/ T.0227

Let us stick with the differentials not the finite.0240

- DH/ T or you can write it in terms of a finite difference, δ S of the surroundings is equal to - Q sub P surroundings.0245

= -δ H/ T, if I want to know what the change in entropy of the surroundings is, not the change in entropy of the system, I just take the δ H of the system.0275

Take the negative side of it and divide by the temperature at which this process is taking place.0289

Since, we have δ S of the surroundings = - δ H/ T, we can solve for the δ H.0299

We are just going to move some things around.0313

We are going to get δ H = - T δ S.0315

I’m going to take this δ H = - T δ S and I'm going to put back in for this δ H.0321

This is what I get, I get δ G = - T δ S of the surroundings - T δ S.0329

This δ S of the system.0344

I get δ G = - T, I’m going to go ahead and factor out - T so I get δ S of the surroundings, the change in entropy of the surroundings + the change in entropy of the system.0348

The change in entropy of the surroundings + the change in entropy of the system that is just a change in entropy of the entire universe,0359

the universe that we are talking about, system + surroundings.0373

What I have is a δ G = - T δ S of the universe.0376

Let me go ahead and move forward here.0386

The pages are a little sticky.0391

Let me rearrange this and I have that the δ S of the universe = - δ G/ T.0393

I just found the δ of the surroundings that was the - δ H of the system ÷ T.0406

The δ of the universe that is just the - δ G of the system ÷ T.0414

When δ G is less than 0, implying a spontaneous process that means δ G = - T δ S that means - T δ S of the universe is less than 0,0424

that means δ S of the universe is greater than 0.0445

In terms of entropy, in order for a process to be spontaneous it is the change in entropy of the entire universe that has to be greater than 0.0450

We express the spontaneity condition using δ G, this is δ G of the system.0460

This is very convenient because basically, we have only have to deal with some property of the system, this change in free energy.0467

As it turns out, the change in free energy, the negative of the divided by the temperature actually gives us the change in entropy of the universe.0474

This is the relationship, δ G is just another way of looking at δ S of the universe.0482

That is what all these relationships say.0488

That is what this says δ G and S of the universe they are actually the same thing that is related by the negative of the temperature.0490

The spontaneity condition with a free energy change has to be less than 00498

is really the same as the change in entropy of the universe has to be greater than 0.0503

We deal with δ G because it is a lot easier to deal with free energy and measure free energy changes than it is to measure entropy changes.0508

But this is the relationship.0516

Let me write that out.0523

For a process to be spontaneous, it is the entropy of the universe that has to be greater than 0.0527

Entropy, not the entropy of the system, it is the entropy of the universe that must be greater than 0.0547

We elucidate it, it was just a very simple mathematics based on the fact that the δ G being less than 0 is the defining property for spontaneity.0563

It turns out that that happens to be that the δ S of the universe has to be greater than 0.0571

The entropy of the system in a spontaneous process can decrease as long as there0576

is a more than compensating increase in the change in entropy of the universe.0582

The entropy of the system can decrease in a spontaneous process as long as there is a more than compensating increase in entropy0591

and the surroundings so that the overall entropy of the universe is greater than 0.0598

Let us write this down.0607

The entropy of the system may decrease during a spontaneous process as long as there is a more than compensating0610

increase in the entropy of the surroundings such that the δ S of the universe which is equal to the δ S of the surroundings + the δ S of the system of this is greater than 0.0653

In other words, δ S of the surroundings + δ S of the system greater than 00697

which means that the δ S of the surroundings is greater than that negative of the δ S of the system.0712

If the system decreases, if the system’s entropy decreases by 10 units, in order for that process to be spontaneous,0720

the change in entropy of the surroundings have to be greater than 10 units.0728

10.1, 10.2, 11, 12,30, whatever, it has to be greater than the decrease in the change in entropy of the system.0733

As long as that is satisfied, as long as this is satisfied, the process is spontaneous.0741

Let us see here, the way I remember everything is the following.0750

This is what makes this particular equation δ G = δ H - T δ S.0754

It is a very important equation.0758

The way that I remember everything is the following.0760

Let me write that out.0765

The way I remember everything is I take the δ G = δ H - T δ S our fundamental equation for that relationship,0768

I go ahead and I divide everything by – T.0787

I get - δ G/ T, I think my negative sign in the middle, I like to just put on the top for the numerator that way it is more consistent, = - δ H/ T + δ S.0791

I have this is δ S of the universe, this is the δ S of the surroundings.0808

Let me write that a little bit better, δ S of the surroundings and this is the δ S of the system.0818

I have my equation and if I need my δ H.0829

I'm sorry, if I need my δ S of the surroundings I just take the negative of the enthalpy of the system divided by the temperature which it take place.0832

If I need the δ S of the universe, I can either add these.0840

If I happen to know this or I can go ahead and take the negative of the free energy change for the equation0843

and divide that by the temperature of which the process is taking place.0849

That and that.0855

Writing out formally, δ S of the universe = - δ G/ T.0865

δ S of the surroundings = - δ H/ T and δ S of the system well that is just δ S system.0877

One final thing regarding this,0893

let us look at a non spontaneous process and verify that this is actually the case.0898

Let us look at a known spontaneous process and you can do this with any spontaneous process.0908

The best example, I did not choose the combustion example but it is probably the best example to choose.0920

I chose the conversion of water vapor to water.0925

Let us look at a non spontaneous process to verify what is it that we have just talked about.0929

We would look at water vapor and 25°C condensing to liquid water.0937

At 25°C, if I have some steam that is going to spontaneously turn into liquid water.0949

Using a table of thermodynamic data, I get the following.0955

I find that the δ H of the reaction was going to be products – reactants.0960

It is going to be -286 and this is kJ/ mol but leave off the units.0967

-242 so we end up getting - 44 kJ/ mol.0975

I will go ahead and put it there.0984

Table of thermodynamic data also includes free energy changes so I can do δ G as well from the table of thermodynamics data.0987

We will only use all the resources of my disposal.0993

The δ G of the reaction is -237 - -229 and that = -8 kJ/ mol.0995

δ G = δ H - T δ S and this is of the system.1012

Therefore, when we arrange this equation to solve for δ S I get the following.1020

I get δ G - δ H ÷ - T = δ S.1026

δ G is -8 - -44 ÷ 298.1036

The table of thermodynamic data, everything is done at 25°C so 298°K.1046

I get -0.121 as my change in entropy of the system.1059

Let us go ahead and do the δ S of the surroundings.1073

The δ S of the surroundings we said that = - δ H/ T.1076

It is going to be - -44/ 298 and I end up with 0.148.1083

Clearly, the change in the surroundings, the 0.148 is greater than the change the 0.121 of the system.1097

The system decreases in entropy by 0.121 but the entropy of the surroundings changed by 0.148.1108

If I take δ S of the universe = the positive 0.148 and I add to that the change in entropy of the system which is -0.121 and I end up with something.1115

The number does not matter, it is positive, it is greater than 0, that is what it confirms.1134

The spontaneous process is a change in entropy of the universe that is greater than 0 not the change in entropy of the system.1139

The change in entropy of the system was negative but together combined with a change in entropy of the surroundings1148

you end up with a change in entropy of the universe being greater than 0.1153

+ 0.027 which is clearly greater than 0.1159

Again, I have I do not know about my arithmetic, you can check it for me but you will find that this number is bigger than absolute value of that number.1165

That is it, thank you for joining us here at www.educator.com.1176

We will see you next time, bye.1179