The 4 Laws of Thermodynamics Simply Explained

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.

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.

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.

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 \( \class{purple}{\Delta W} \):

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.

• 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.

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).

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: \( \Delta S_{\text u} = \class{red}{\Delta S} + \class{green}{\Delta S_{\text e}} \).

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.

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.