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.
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:
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 = 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.
The Four Laws, Compared
| Law | Statement (In Brief) | Real Discoverer(s) | Real Year |
|---|---|---|---|
| Zeroth | Two systems in equilibrium with a third are in equilibrium with each other | Ralph H. Fowler | 1930s |
| First | Energy is conserved: ΔU = Q − W | Clausius, Kelvin (building on Joule) | ~1850 |
| Second | Total entropy never decreases | Sadi Carnot (roots); Clausius (entropy) | 1824 |
| Third | Entropy approaches a constant as T → 0 K | Walther Nernst | 1906–1912 |
Hands-On Exercises
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