Alexander Fufaev
My name is Alexander FufaeV and here I will explain the following topic:

The 4 Laws of Thermodynamics Simply Explained

Formula

Formula: First Law of Thermodynamics
Change in the Internal Energy of a System
What do the formula symbols mean?

Internal energy

Unit
Change of internal energy \(\Delta U=U_2-U_1 \) of a system (e.g. a gas) is the sum of the amount of heat \(Q\) and the work \(W\) done.

Thermal energy

Unit
Thermal energy (heat) added to the system (\(\class{orange}{\Delta Q}>0\)) or released from the system (\( \class{orange}{\Delta Q}< 0 \)).

Work

Unit
Work done ON the system (\( \class{purple}{\Delta W} > 0\)) or work done BY the system (\(\class{purple}{\Delta W} < 0\)).
Explanation
Table of contents
  1. Formula
  2. The zeroth law of thermodynamics
  3. The first law of thermodynamics
  4. The second law of thermodynamics
  5. The third law of thermodynamics

Video

The basis of the whole thermodynamics are the four laws of thermodynamics. With the help of these laws mankind is able to...

  • Converting heat into electrical and mechanical energy is what happens, for example, in nuclear power plants.

  • Transfer heat efficiently. This happens in your refrigerator or air conditioner.

  • To improve the thermal cycle in combustion engines and enhance their efficiency.

  • To control and optimize chemical reactions.

  • To quantitatively understand the phase transitions (such as from liquid to gas) of different substances.

  • To predict climate change and weather.

It is therefore extremely important to understand the four laws of thermodynamics if you want to delve deeper into the aforementioned points or similar topics. So, grab your favorite warm drink ☕ and let me explain the four laws to you as simply as possible.

One thing should be noted: The laws of thermodynamics are based on an incredibly solid empirical foundation that is experimentally confirmed on a daily basis. However, these laws cannot be mathematically proven!

The zeroth law of thermodynamics

Let's consider three cuboid-shaped, isolated systems A, B, and C. These systems do not allow matter to enter or leave. On one side, each system is not isolated, but rather closed. On this side, energy exchange is possible.

  • Let's bring systems A and B into thermal contact on the side where the systems are closed. Now, heat exchange can occur between the two systems. We assume that systems A and B are in thermal equilibrium. Two systems are in thermal equilibrium when they do not exchange energy through thermal contact.

  • Let's bring systems B and C into thermal contact in the same way. Again, we observe that they are in thermal equilibrium.

The zeroth law of thermodynamics predicts that also systems A and C are in thermal equilibrium. We don't need to bring them into thermal contact to know that.

fufaev.org The Zeroth Law of Thermodynamics for Systems A, B and C in Thermal Contact
The systems (A and B) as well as (B and C) are in thermal contact and thermal equilibrium. According to the zeroth law of thermodynamics, we know that (A and C) must also be in thermal equilibrium.

Let us summarize the statement of the zeroth law of thermodynamics:

IF (A in thermal equilibrium with B) AND (B in thermal equilibrium with C) THEN (A in thermal equilibrium with C).

The zeroth law suggests that there is a thermodynamic quantity that characterizes the thermal equilibrium of two systems. We call this quantity temperature \(T\).

If two systems A and B are in thermal equilibrium, they have the same temperature: \( T_{\class{brown}{\text A}} = T_{\class{purple}{\text B}} \). If temperature equality characterizes thermal equilibrium, then we can conclude from the zeroth law:

IF     \( T_{\class{brown}{\text A}} = T_{\class{purple}{\text B}} \)     AND     \( T_{\class{purple}{\text B}} = T_{\class{violet}{\text C}} \)     THEN     \( T_{\class{brown}{\text A}} = T_{\class{violet}{\text C}} \).

The zeroth law (transitivity of thermal equilibrium) may seem trivial when observed in our everyday lives, but it is crucial for the mathematical foundation of thermodynamics.

The first law of thermodynamics

You surely know the law of conservation of energy from mechanics, which states that the total energy \( W \) of a system does not change over time, that is, it is constant: \( W = \text{const.} \)

The total energy of a system is equal to its internal energy \( U \). The internal energy of a system, such as a metal cube, is composed of the sum of the kinetic energies of all the particles that make up the metal cube, as well as their potential energies due to mutual electric repulsion or attraction. This internal energy remains constant over time; it neither increases nor decreases. This condition is satisfied when the system, in this case the metal cube, does not transfer energy to the surroundings. The metal cube must be an isolated system in order for the internal energy to remain unchanged.

Formula anchor

If the internal energy changes, this is an indication that the system is not isolated. The kinetic and/or potential energy of the particles of the metal cube either increases or decreases over time.

The internal energy of a system can be changed in two ways:

  1. By supplying or releasing thermal energy (heat) \( \class{orange}{\Delta Q} \).

  2. By the work done on or by the system \( \class{purple}{\Delta W} \).

The difference \( \Delta U = U_2-U_1 \) of internal energy from the initial value \( U_1 \) to the final value \( U_2 \) is the amount of thermal energy dissipated or supplied \( \class{orange}{\Delta Q} \) PLUS the amount of work done \( \class{purple}{\Delta W} \):

Formula anchor

The most common way to increase the internal energy of a system is by heating it, which means increasing the system's temperature. In doing so, we supply the system with thermal energy \( \class{orange}{\Delta Q} \). Another way is by applying mechanical pressure to the system, which results in work \( \class{purple}{\Delta W} \) being done on the system.

fufaev.org Change in the Internal Energy of a System
Change in the Internal Energy of a System
  • If the change \( \class{orange}{\Delta Q} \) in thermal energy is positive: \( \class{orange}{\Delta Q} > 0 \), you can imagine that thermal energy is "flowing into" the system. If it is negative: \( \class{orange}{\Delta Q} < 0 \), then thermal energy is "flowing out" of the system (see illustration 2).

  • If work \( \class{purple}{\Delta W} \) is positive: \( \class{purple}{\Delta W} > 0 \), then work is done ON the system. The internal energy increases. And if the work is negative: \( \class{purple}{\Delta W} < 0\), then work is done BY the system. The internal energy decreases.

Example: Change of the internal energy of a metal cube

A metal cube has an internal energy of 100 joules. 50 joules are supplied to the metal cube by compressing it. At the same time, the metal cube loses 30 joules by giving off heat. By how much has the internal energy changed and what is its new internal energy?

We use Eq. 2 for the change in internal energy:

Formula anchor

The new internal energy \( U_2 \) of the cube after these processes is its initial internal energy \( U_1 \) plus the change \( \Delta U \) of internal energy:

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The second law of thermodynamics

The second law of thermodynamics introduces a third essential quantity in addition to temperature and internal energy, which is entropy \( S \).

At the macroscopic level, the generated amount of entropy \( \class{red}{\Delta S} \) (change in entropy) is the ratio of the thermal energy \( \class{orange}{\Delta Q} \) transferred to or from the system to the temperature \( T \) at which this process occurs. The unit of entropy is therefore J/K (Joule per Kelvin).

The second law: Increase of the entropy of the universe

After every spontaneous process in the universe, the entropy \( S_{\text u} \) of the universe increases. This means that the change in entropy \( \Delta S_{\text u} \) of the universe is always positive for spontaneous processes: \( \Delta S_{\text u} > 0 \).

A spontaneous process is a process that naturally occurs on its own. An example of a spontaneous process is the reaching of the thermal equilibrium between two systems. When a hot body is brought into thermal contact with a cold body, the temperatures of the two bodies equalize. No energy input is required for this spontaneously occurring process. In such a process, the entropy of the universe increases.

What exactly is meant by "universe"? In thermodynamics, the term "universe" refers to the system with its surroundings. In the above example, the cold and hot bodies represent the system, while their surroundings are the medium in which the two bodies are situated, such as the air. The entropy change of the \( \Delta S_{\text u} \) is therefore composed of the entropy change \( \class{red}{\Delta S} \) of the system and the entropy change \( \class{green}{\Delta S_{\text e}} \) of the surroundings: \( \Delta S_{\text u} = \class{red}{\Delta S} + \class{green}{\Delta S_{\text e}} \).

fufaev.org Entropy Change of the System, the Surroundings and the Universe
Entropy Change of the System, the Surroundings and the Universe

According to the second law: \( \class{red}{\Delta S} + \class{green}{\Delta S_{\text e}} > 0 \) for spontaneous processes. It is allowed for the entropy change \( \class{red}{\Delta S} \) of the system or the entropy change \( \class{green}{\Delta S_{\text e}} \) of the surroundings to be individually negative. Only their sum must always be positive! For example, when water freezes, the entropy \( \class{red}{\Delta S} \) of the water decreases: \( \class{red}{\Delta S} < 0 \), but the entropy change \( \class{green}{\Delta S_{\text e}} \) of the surroundings increases, by a greater magnitude, so that \( \class{red}{\Delta S} + \class{green}{\Delta S_{\text e}} > 0 \) is fulfilled.

Example: Water becomes gaseous

A container of water is heated, causing the water to undergo a phase transition and turn into a gaseous state. During this process, 200 joules of thermal energy are supplied to the water. The temperature of the water remains constant at 300 Kelvin because the energy is being utilized for the phase transition. How large is the entropy change of the water?

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The third law of thermodynamics

What happens to the entropy \( \class{red}{S}\) of a closed system when the system is attempted to cool to absolute temperature zero (\(T = 0\,\mathrm{K}\))?

The third law of thermodynamics (also known as the Nernst theorem) states that the change in entropy \( \class{red}{\Delta S} \) of a closed system approaches zero as the temperature \( T \) approaches absolute zero.

Theoretically, if we could cool a system to \(T = 0\,\mathrm{K}\), then \( \class{red}{\Delta S} = 0\). This means that the entropy \( \class{red}{S} \) of the system would reach a constant \( \class{red}{S} = S_0 \). Once we have reached \(0\,\mathrm{K}\), there is no way back. If a system has already reached absolute zero, no further thermal energy \( \class{orange}{\Delta Q} \) can be supplied to it to increase its temperature. The system would simply absorb the supplied energy without any change in temperature.

The third law of thermodynamics thus establishes a fundamental limit, stating that the absolute zero temperature cannot be reached, and at this temperature, the entropy of a system reaches a minimum value.

Third law of thermodynamics: Absolute zero point

The absolute zero point \( T = 0\,\mathrm{K} \) cannot be reached.