The Laws of Thermodynamics

Classical Mechanics & Thermodynamics
Course 1 · Chapter 7 · The Laws of Thermodynamics

Chapters 1–6 covered mechanics — motion, force, energy, and gravity applied to objects you can point at. This chapter opens the course's second half, thermodynamics: the same conservation-of-energy thinking from Chapter 3, now applied to heat, temperature, and the countless untrackable microscopic motions inside ordinary matter.

Four Laws, Numbered Out of Historical Order

Thermodynamics has four laws, numbered zeroth through third — and that numbering genuinely does not reflect the real order they were discovered in. The real, documented history runs almost entirely backward from the numbering:

  • The Second Law came first, in 1824, when French engineer Sadi Carnot analysed the theoretical limits of steam engine efficiency.
  • The First Law was formalised next, by around 1850, through the combined work of Rudolf Clausius and William Thomson (later Lord Kelvin) — building directly on James Prescott Joule's own 1842–1845 experiments, including the paddle-wheel apparatus already covered in Chapter 3.
  • The Third Law came third, formulated by German chemist Walther Nernst between 1906 and 1912.
  • The Zeroth Law came last of all, identified only in the 1930s by physicist Ralph H. Fowler.
💡 Why "Zeroth"? Fowler's own 1930s law turned out to state something so basic — a precondition for temperature itself to be a meaningful concept — that it logically had to come before the other three, even though it was discovered decades after them. Rather than renumber the three already-established, already-famous laws, physicists gave the newcomer the number zero instead, so it could sit first in the logical order without disturbing everything already built around "first," "second," and "third." A genuinely counterintuitive piece of real numbering history, and a good match for this course's own recurring theme (Galileo's tower, "Newton's cradle," and Newton's apple) of the tidy popular version differing from the messier real one.

The Zeroth Law: What Temperature Actually Means

The Zeroth Law states: if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. "Thermal equilibrium" simply means no net heat flows between two systems in contact — they are at the same temperature.

This sounds almost too obvious to bother stating, but it is exactly what makes a thermometer meaningful at all. A thermometer is the "third system": if it reads the same temperature in contact with your morning coffee as it did in contact with a reference standard, the Zeroth Law is what licenses the conclusion that the coffee and the reference standard are themselves at the same temperature — without ever placing the coffee and the reference in direct contact.

The First Law: Conservation of Energy, for Heat and Work

The First Law is Chapter 3's own conservation of energy, extended to include heat as a genuine form of energy transfer alongside mechanical work:

ΔU = Q − W

Here ΔU is the change in a system's internal energy, Q is heat added to the system, and W is work done by the system on its surroundings. Chapter 3's own worked example — Joule's falling weight turning a paddle wheel inside an insulated barrel of water — is exactly a First Law demonstration: with the tank thermally isolated (no heat escaping, Q = 0) and mechanical work put in by the descending weight, the water's own internal energy rose by precisely that amount of work, measured directly as a real, reproducible temperature increase.

Worked Example: Heating and Expanding Gas

500 J of heat is added to a gas in a cylinder. As it warms, the gas expands and does 200 J of work pushing a piston outward. What is the change in the gas's internal energy?

ΔU = Q − W
ΔU = 500 − 200
ΔU = 300 J

Of the 500 J of heat supplied, 200 J left the system again as mechanical work on the piston, leaving a net 300 J increase in the gas's own internal energy — energy is neither created nor destroyed, only moved and converted, exactly as Chapter 3's conservation of energy already established.

The Second Law: A Preview

The Second Law states that the total entropy of an isolated system never decreases — only stays the same or increases over time. Entropy, loosely, measures how spread out or disordered a system's energy has become. This law is what gives many everyday processes a real, one-way direction: heat flows from hot objects to cold ones, never spontaneously the reverse; a dropped egg scrambles, but never un-scrambles itself. Chapter 8 (Heat Engines & Entropy) covers this law in far more depth, including the real Carnot cycle Sadi Carnot's own 1824 work — already mentioned above as the true historical starting point of this whole chapter — was built to analyse.

The Third Law: Absolute Zero Is Approached, Never Reached

The Third Law states that a system's entropy approaches a fixed, minimum value as its temperature approaches absolute zero — 0 K, equal to −273.15°C, the theoretical coldest possible temperature. A real, direct consequence of this law is that absolute zero itself can never actually be reached by any real physical process in a finite number of steps, no matter how effective the cooling method — only approached asymptotically, ever more closely but never quite arriving.

âš  How Close Has Anyone Actually Gotten? In a real 2021 laboratory experiment, scientists cooled a cloud of rubidium atoms to just 38 picokelvin — 38 trillionths of one kelvin above absolute zero — using a technique called matter-wave lensing on a Bose–Einstein condensate. Even this extraordinary, genuinely record-setting result stayed strictly above 0 K, exactly as the Third Law predicts it always must.

The Four Laws, Compared

LawStatement (In Brief)Real Discoverer(s)Real Year
ZerothTwo systems in equilibrium with a third are in equilibrium with each otherRalph H. Fowler1930s
FirstEnergy is conserved: ΔU = Q − WClausius, Kelvin (building on Joule)~1850
SecondTotal entropy never decreasesSadi Carnot (roots); Clausius (entropy)1824
ThirdEntropy approaches a constant as T → 0 KWalther Nernst1906–1912

Hands-On Exercises

Exercise 1
A gas in a sealed, rigid container is heated, receiving 800 J of heat. Because the container is rigid, the gas cannot expand and does zero work on its surroundings (W = 0). Using the First Law, calculate the change in the gas's internal energy.
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Exercise 2
Three metal blocks, A, B, and C, are tested with a thermometer. Block A and Block C both read exactly 25 degrees Celsius on the thermometer. Using the Zeroth Law, what can you conclude about the thermal relationship between Block A and Block C directly, without ever placing them in contact with each other?
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Exercise 3
Explain, in your own words, why the Zeroth Law is numbered "zero" rather than being called the "Fourth Law" - and why this numbering is a real, documented piece of scientific history rather than an arbitrary naming choice.
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Quick Reference

  • Zeroth Law: systems in equilibrium with a common third system are in equilibrium with each other (defines temperature)
  • First Law: ΔU = Q − W (conservation of energy for heat and work)
  • Second Law: total entropy never decreases (covered in depth in Chapter 8)
  • Third Law: entropy approaches a constant as temperature approaches absolute zero (0 K = −273.15°C), which is never actually reached
  • Real discovery order: Second (1824) → First (~1850) → Third (1906–12) → Zeroth (1930s) — the exact reverse of the numbering

Next chapter: Heat Engines & Entropy — where Sadi Carnot's real 1824 work, already introduced here as the true historical root of the Second Law, gets its full, in-depth treatment.