Thermodynamics Laws: Universal Or Not?

The laws of thermodynamics are a set of scientific laws that define a group of physical quantities, such as temperature, energy, and entropy, that characterise thermodynamic systems in thermodynamic equilibrium. Traditionally, there are three fundamental laws: the first law, the second law, and the third law. However, a more fundamental statement was later added and labelled as the zeroth law after the first three laws had been established. The first law of thermodynamics is the familiar conservation of energy principle, which states that energy can neither be created nor destroyed. The second law of thermodynamics states that while energy is conserved, it becomes less useful over time as it spontaneously converts thermal energy into mechanical work. The third law of thermodynamics states that a system's entropy approaches a constant value as its temperature approaches absolute zero. The laws of thermodynamics are well-established and appear to apply universally, but do they apply to the universe as a whole?

The First Law of Thermodynamics

> ΔU = Q - W

Where ΔU is the change in the internal energy of the system, Q is the quantity of heat supplied to the system from its surroundings, and W is the quantity of energy gained or lost through thermodynamic work.

The Second Law of Thermodynamics

The second law states that there exists a useful state variable called entropy. Entropy has a variety of physical interpretations, including the statistical disorder of a system. For the purposes of this explanation, entropy can be considered another property of a system, like enthalpy or temperature.

The second law states that the change in entropy (delta S, \(\Delta S\)) is equal to the heat transfer (delta Q, \(\Delta Q\)) divided by the temperature (T). This can be expressed as:

\(\LARGE \Delta S=\frac{\Delta Q}{T})

For a given physical process, the entropy of the system and the environment will remain constant if the process can be reversed. If we denote the initial and final states of the system by “i” and “f”, then:

\(\LARGE S_{f}=S_{i}(\text{reversible process})\)

An example of a reversible process is ideally forcing a flow through a constricted pipe. As the flow moves through the constriction, the pressure, temperature, and velocity would change, but these variables would return to their original values downstream of the constriction. The state of the gas would return to its original conditions, and the change in entropy of the system would be zero.

The second law states that if the physical process is irreversible, the entropy of the system and the environment must increase; the final entropy must be greater than the initial entropy. This can be expressed as:

\(\LARGE S_{f}>S_{i}(\text{irreversible process})\)

An example of an irreversible process is when a hot object is put in contact with a cold object. Eventually, they both achieve the same equilibrium temperature. If we then separate the objects, they do not naturally return to their original (different) temperatures. The process of bringing them to the same temperature is irreversible.

The second law can be stated in any of three synonymous ways:

• For a spontaneous process, the entropy of the universe increases.
• For a spontaneous process, ΔSuniverse > 0.
• For a spontaneous process, ΔSsystem + ΔSsurroundings > 0

Ultimately, for any spontaneous process, the entropy, which is related to randomness or disorder, of the universe increases.

The Third Law of Thermodynamics

A perfect crystal refers to a system with no impurities that has achieved thermodynamic equilibrium. It is in a crystalline state where all the atoms, ions, and molecules are in well-defined positions in a highly ordered crystalline lattice. This excludes amorphous solids like glass, which lack an ordered, crystalline structure and have not achieved thermodynamic equilibrium.

> S – S0 = 𝑘B ln𝛀

Where:

• S is the entropy of the system.
• S0 is the initial entropy.
• 𝑘B denotes the Boltzmann constant.
• 𝛀 refers to the total number of microstates that are consistent with the system's macroscopic configuration.

For a perfect crystal with exactly one unique ground state, 𝛀 = 1, so the equation simplifies to:

> S – S0 = 𝑘B ln(1) = 0 [because ln(1) = 0]

When the initial entropy of the system is set to zero, the following value of 'S' is obtained:

> S – 0 = 0 ⇒ S = 0

Thus, the third law of thermodynamics states that the entropy of a perfect crystal at absolute zero is zero.

The third law also has several alternate statements, including:

• The Nernst statement, which implies that it is impossible for any process to bring the entropy of a given system to zero in a finite number of operations.
• The statement by American physical chemists Merle Randall and Gilbert Lewis, which says that when the entropy of each element in a perfect crystalline state is taken as zero at absolute zero temperature, every substance has a finite, positive entropy. However, the entropy at absolute zero can be zero, as in the case of a perfect crystal.
• The Nernst-Simon statement, which can be written as: "For a condensed system undergoing an isothermal process that is reversible in nature, the associated entropy change approaches zero as the associated temperature approaches zero."
• Another implication is that the exchange of energy between two thermodynamic systems (whose composite constitutes an isolated system) is bounded.

The third law has important applications, such as calculating the absolute entropy of a substance at any temperature 'T'. These calculations are based on heat capacity measurements of the substance.

In summary, the third law of thermodynamics provides a reference point for understanding the behaviour of systems at absolute zero, with implications for entropy, energy, and temperature.

The Zeroth Law of Thermodynamics

Two systems are said to be in thermal equilibrium if they are linked by a wall permeable only to heat, and they do not change over time. This law is important for the mathematical formulation of thermodynamics, as it justifies the use of practical thermometers. It establishes thermal equilibrium as an equivalence relationship, allowing any member of a subset to be uniquely "tagged" with a label identifying the subset to which it belongs. Temperature is just such a labeling process, using the real number system for tagging.

The Zeroth Law provides an independent definition of temperature without reference to entropy, which is defined in the second law. It is based on temperature measurement and states that "systems that are in thermal equilibrium exist at the same temperature". This law is particularly useful for comparing the temperatures of different objects. For example, if we want to measure the accurate temperature of an object, we can bring it into contact with a reference body, and observe how a certain characteristic of the body changes with temperature. This change can be taken as an indication of a change in temperature, and the selected characteristic is known as a thermodynamic property.

The Zeroth Law also has applications in the creation of thermometers. For instance, a mercury-in-glass thermometer utilizes the fact that mercury expands as temperature increases, leading to an increase in the height of the mercury in the tube. This increase in height can then be used to measure the changes in temperature.

In summary, the Zeroth Law of Thermodynamics is a fundamental principle in thermodynamics that defines thermal equilibrium and provides a basis for temperature measurement and the creation of practical thermometers.

The Origin of the Universe

The laws of thermodynamics play a crucial role in understanding the origin of the universe. The first law of thermodynamics states that energy cannot be created or destroyed, only transformed. This means that the total amount of energy in the universe has always been and will always be constant. However, this law applies only to closed systems, and the universe itself is not a closed system. It is essential to recognize that the laws of thermodynamics, as we understand them, may not apply to the extreme conditions present during the birth of the universe.

The second law of thermodynamics states that the entropy of the universe, or the level of disorder, tends to increase over time. This law suggests that the universe could not have existed infinitely and must have had a beginning. However, this conclusion contradicts the implication of the first law, which states that the universe must be eternal for energy to be conserved.

This contradiction has led to discussions about the nature of the universe and the possibility of a creator or external influence. Some argue that the universe is not an isolated system and that external factors could have played a role in its creation. Others suggest that the laws of thermodynamics, as we understand them, may not apply to the universe as a whole.

While the origin of the universe remains a subject of ongoing scientific investigation and philosophical debate, it highlights the complexities and limitations of our current understanding. It prompts us to explore the intersection of science and metaphysics, seeking answers to questions that challenge our comprehension of the cosmos.

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