The word "entropy" and the phrase "law of thermodynamics" are increasingly encountered today - in books, movies, the Internet. But few people know what these concepts mean and what processes they describe.

Can the engine run at 100% efficiency? In 1824, a scientist named Nicolas Leonard Sadi Carnot, also known as the "father of thermodynamics", tried to answer this question. In one of his theoretical models, he placed a cylinder with a piston between two heat reservoirs. Both tanks kept a constant temperature, but the temperature of one of them was higher than that of the other.

The idea was to convert the heat flow between the two tanks into work. It was for this that Carnot placed a cylinder with a piston between the reservoirs. However, he realized that it would not be possible to achieve 100% performance: some of the heat always went through the cylinder into the cold tank.

The first law of thermodynamics states that energy cannot be created or destroyed - it can only change its shape. But there are some limitations. The law does not define the direction in which a change can occur, and does not indicate the reversibility of this change. If we throw an object off the elevation, potential energy is transformed into kinetic energy, and it falls. However, after hitting the ground, it will not bounce back to the same height from which it fell. Why it happens? To understand this, it is necessary to consider an important term - spontaneous process.

## Spontaneous process

A spontaneous process in thermodynamics is a process that can occur without any outside interference: it must have enough time for this. Drop ink into a glass of water - it will "spontaneously" spread throughout the glass, while sugar must be stirred to dissolve. When it's hot outside, the room heats up "spontaneously", but you need an air conditioner to cool it down.

From our own experience, we know that some of the events that take place in our lives are spontaneous. However, scientists had to find a way to determine the spontaneity of any event. They needed a way to determine the direction in which the change was taking place. This very need has given rise to what today we call the second law of thermodynamics.

## The second law of thermodynamics

The laws of thermodynamics determine how work, heat and energy affect any system. A system is any limited area in the universe through which energy can be transferred. Anything outside this system is considered its environment.

The second law of thermodynamics states that in a spontaneous process, the total entropy of the Universe always increases. What is entropy?

## Entropy

If you've never come across this term before, you might associate it with "disorder." However, in thermodynamics, the definition of entropy is slightly more detailed.

First of all, in order to understand what entropy is, one must understand that all energies are quantized. When electrons in an atom receive energy, they only absorb it in whole multiples of a small amount of energy called a "quantum."

When a drop of ink falls into a glass of water, it spreads through the liquid. Likewise, if you have a piece of hot metal on your table, its heat spreads throughout its environment. Imagine that you have a box of five gas molecules next to this piece of metal. The metal will transfer five quanta of heat to the gas.Will each gas molecule receive one quantum of energy? Not necessary.

It is quite possible that two molecules will receive two quanta, and one only one, while the other two units will receive nothing at all. It is possible that one molecule will receive three quanta, the other two, and the rest nothing.

In this case, there are as many as 126 possible combinations of the process of transferring quanta of heat

These gas molecules can also collide with each other and exchange kinetic energy. However, the total energy cannot exceed the amount of energy provided to the system.

Each of these combinations is called a microstate. The total energy level is called a macro state. Entropy is a measure of the probabilities of energy distribution between molecules.

Entropy is a state variable that describes the physical state of a system - like pressure, temperature, and volume. Entropy can be explained by the following mathematical formula: S = k_{B}lnΩ, where S is the entropy, k_{B}is Boltzmann's constant, Ω is a measure of probability. Boltzmann's constant is a physical constant that determines the average kinetic energy of gas particles in relation to temperature. To calculate the entropy, this constant is multiplied by the natural logarithm of the number of microstates (a measure of probability).

The change in entropy can also be calculated by dividing the heat received by the temperature. The resulting heat increases the kinetic energy of the particles.

Essentially, entropy is the number of ways in which energy is distributed between molecules in a system.

## Heat engine entropy

Let's return to the Carnot engine and try to find out under what conditions a heat engine is possible. Suppose that the temperature of the hot tank is T_{H}, and the temperature of the cold reservoir is T_{C}… Heat quantity Q_{H}retrieved from the reservoir to perform work.

Thus, the change in entropy in a hot tank can be calculated using the following formula: ΔS_{H} = -Q_{H} / T_{H}

Q is negative, as heat is extracted from the reservoir.

After the work is done by the piston in the engine and its return to its initial state, the change in the entropy of the engine (ΔS_{E}) will have a value of 0.

If we assume that all the energy is used to do the work, and the cold reservoir does not receive any heat at all, then the entropy of the cold reservoir (ΔS_{WITH}) will also have a value of 0.

Hence:

The total entropy of the Universe becomes negative, which means that it cannot be spontaneous.

Now suppose the cold reservoir receives the amount of heat Q_{C} and is not used to do the job. In this case, the entropy of the cold reservoir: (ΔS_{C}) - Q_{C} / T_{C}.

So we get the following:

The only case in which the engine can work is when the entropy of the Universe (ΔS_{universe}) is positive or if the value of Q is positive_{C} / T_{C} - Q_{H} / T_{H}, as the second law of thermodynamics says.

## Universal law

The second law of thermodynamics drives the universe. We know that the universe is expanding. According to the second law of thermodynamics, the entropy of the universe should also increase. Stars are the source of energy for the universe. By the time the last star emits its last photon, the level of entropy will be incredibly high. You should not worry about this: we will all go into oblivion long before that. Then the Universe will perish, since there will be no more energy left to increase its entropy.