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#### 理解热力学第二定律

Understanding Second Law of Thermodynamics !

The second law of thermodynamics is a fundamental law of nature,

unarguably one of the most valuable discoveries of mankind.

However, this law is slightly confusing

for most engineers or students.

The main reason for this is

because it has so many complex terms in it,

and that there are many ways that this second law

can be stated, but most importantly,

the majority do not understand

what are the applications of this law.

In this video we will create a real,

physical insight into this law,

with a minimum use of mathematics.

The million dollar question is,

for what purpose is this law used.

One of the main uses of the second law of thermodynamics

is to determine whether a process is spontaneous or not.

Let’s consider a few examples.

Here two gases are mixing together, air is being leaked

from a balloon, and the mass is falling down,

and the hot tea is losing its heat.

You can see that the process of moving from state 1

to state 2, will happen spontaneously,

which means without any external aid.

But what about the opposite process?

Will that happen spontaneously?

Would this mixed gas become unmixed

spontaneously without any external aid?

From your own experience,

you know this will not happen.

So this process is not spontaneous.

However, according to the rules of energy conservation,

or the first law of thermodynamics,

even the reverse process is possible.

because in both states, the energy is the same.

So what is missing here?

There must be one more law

which governs the direction of a process,

and that law is second law of thermodynamics.

Now probably you have a question in your mind.

Do I really require a law just to

predict the direction of a process?

I can predict the direction of all these processes

just from my intuition.

If you do have such questions in your mind,

let us analyze one more example.

This is a chemical reaction.

Here I am putting two chemicals together in a chamber,

and I am waiting for a reaction to happen.

I want to check if two blue atoms react

with one yellow atom to form a new molecule.

Do you have an answer for this?

This cannot be predicted through intuition.

This is exactly what the second law is used for.

In this video, we will review the second law.

We will learn it well,

and we will come back to this same problem,

to this chemical reaction.

Here are the two standard definitions of the second law

You may have already heard of them

Both these statements mean the same

but they are not in the state directly useful to engineers.

Here is a useful form of the second law,

that is useful for engineers.

The Clausius Inequality.

This is a small integral equation,

but with deep inner meanings

We will conduct a physical experiment to understand it.

the Clausius inequality means that

if you take a cyclic process, such as in a refrigerator,

and that all the heating action happening at the boundary

divided by the temperature of the boundary

the resulting value will be less than, or equal to zero

This is an interesting inequality,

which is true for all cyclic processes.

To make this equation more application oriented,

let us introduce a new term: the famous term of entropy.

Entropy has two parts, one to represent disorder,

and the other to describe the heat transfer effect.

Here’s a common mythbuster.

Entropy is not only disorder, but it has

one more part within it, that of heat transfer.

In short, entropy change of process can be defined as

the sum of the change in the entropy production and entropy transfer.

For a perfectly reversible process,

when the process has no friction and mixing,

the entropy production becomes zero.

If you use this definition of entropy

and the Clausius inequality,

We can prove mathematically that

during this spontaneous process,

the entropy of the universe always increases.

This is known as the “increase in entropy principle”.

This is a very useful form of the second law.

Now let’s take a practical case

to understand this principle better.

Consider this hot tea problem.

We want to find out whether the hot tea

will absorb or release heat.

The tea is the system,

and everything except the tea is the surroundings.

Assuming the tea is absorbing the heat, a heat of 10J,

so entropy change of hot tea

is 10 divided by temperature of the hot tea.

The same heat amount is lost by the surroundings,

so the entropy change of the surroundings is

minus 10 divided by the temperature of surroundings.

If you add these two quantities,

you will get the entropy change of the universe.

It’s a negtive quantity in this case.

This is impossible due to the second law.

Now, assume the hot tea is losing heat.

So Q will be minus 10 in this case.

You can see that the entropy change of the universe

is positive here, and this is possible.

So using the second law of thermal dynamics.

We are proved that the hot tea can only release heat,

and it cannot absorb heat.

Now let’s get back to the chemical reaction problem.

Assume the reaction has happened,

and the system’s entropy is increased by delta S.

And it has absorbed some heat.

We call it enthalpy.

What we have to calculate is the entropy change of the universe.

We already have the entropy change of the system here.

What will be the value of entropy change of the surroundings?

Here is a small clue for that.

If the system has absorbed some amount of heat,

the surroundings have lost the same amount of heat.

So the entropy change of the surroundings

is negtive delta H divided by T.

Thus you can easily represent the entropy change

of the universe like this.

If this quantity is greater than zero,

then this reaction is feasible.

Now, let’s have a rearrangement of this equation.

Since the temperature T is always posotive,

if I multiply it by minus T,

the inequality equation will become like this.

When this term is less than or equal to zero,

this process is possible.

We call this new term “Gibbs free energy”.

Or in simple words, the change of Gibbs free energy

of the system is less than or equal to zero,

then that process is possible.

This is the advantage of using Gibbs free energy.

Unlike the “increase in entropy ptinciple”, you need not

to worry about what is happening in the surroundings.

You can concentrate your study only on the system.

In this way, you can predict whether a process

is spontaneous or not.

We hope from this video you have developed good

insight into the second law of thermal dynamics.

Thank you for watching the video.

Imagist