The Laws of Thermodynamics

The four laws at a glance

The laws were discovered out of order, which is why the first one is called the zeroth. Together they say what can and can’t happen whenever energy moves as heat.

1. 0

   The zeroth law temperature

   If two things are each in thermal equilibrium with a third, they are in thermal equilibrium with each other.

   T_A = T_C and T_B = T_C
   ⟹ T_A = T_B

   Everyday: a fever thermometer comes to your temperature under your tongue, then tells you what it is. That only works because equilibrium is passed along.

   Chapter 1: Temperature and the Zeroth Law →
2. 1

   The first law energy

   Energy is conserved. The internal energy of a system changes only by the heat that flows in and the work it does.

   ΔU = Q − W

   Everyday: rub your hands together and the work you do becomes internal energy: they warm up. Squeeze a bike pump and the air inside heats up with no flame at all.

   Chapter 2: Energy and the First Law →
3. 2

   The second law entropy

   The entropy of an isolated system never decreases. Heat flows by itself only from hot to cold.

   ΔS ≥ 0  ·  η ≤ 1 − T_c/T_h

   Everyday: an ice cube melts in a glass of lemonade; the lemonade never freezes itself while the room warms up. And no engine can turn all of its heat into work.

   Chapter 3: Entropy and the Second Law → Chapter 4: Engines, Refrigerators and Heat Pumps →
4. 3

   The third law absolute zero

   You can’t reach absolute zero in a finite number of steps, and a system’s entropy approaches a constant as its temperature approaches absolute zero.

   T → 0 K:  S → constant

   Everyday: each step of cooling gets harder than the last. Labs have cooled atoms to within a billionth of a degree of absolute zero, but never all the way.

   Chapter 5: Absolute Zero and the Third Law →

The chapters

1. 1 🌡️ Temperature and the Zeroth Law Press copper, iron, granite, water and wood together and watch heat flow until they share one temperature. ✓ Done
2. 2 ⚙️ Energy and the First Law Heat, squeeze and stretch a gas, trace its P–V path, and watch ΔU = Q − W balance to the joule. ✓ Done
3. 3 🎲 Entropy and the Second Law Run a gas backward and watch it un-spread, nudge one atom by a billionth and watch the trick fail, and play Maxwell’s demon. ✓ Done
4. 4 🚂 Engines, Refrigerators and Heat Pumps Run Carnot’s ideal engine with heat and work drawn to scale, then run it backward as a heat pump, and watch a Stirling engine run on coffee. ✓ Done
5. 5 ❄️ Absolute Zero and the Third Law Climb down a cooling ladder that never reaches the bottom, evaporate atoms into a Bose–Einstein condensate, and zoom a thermometer from picokelvins to fusion plasma. ✓ Done

Key equations

The whole unit on one sheet. Temperatures in these formulas are in kelvins unless they appear only as a difference, ΔT, which is the same in kelvins and degrees Celsius.

A short history

1. 1780s

   Caloric. Heat is pictured as an invisible, weightless fluid, “caloric,” that flows from hot things to cold ones. The idea explains a lot, and Antoine Lavoisier lists it among the elements.

2. 1798

   Rumford bores cannon. In Munich, Benjamin Thompson, Count Rumford, grinds a blunt borer inside a cannon barrel sunk in water, and boils the water by friction alone. Heat seems to come without limit, so he argues it must be motion, not a substance.

3. 1824

   Carnot’s engine. Sadi Carnot publishes Reflections on the Motive Power of Fire. He imagines a perfect, reversible engine and shows that its work depends on the temperatures it runs between: the seed of the second law.

4. 1840s

   Joule’s paddle wheel. James Prescott Joule lets falling weights churn water and measures the tiny rise in temperature: a fixed amount of work always makes the same amount of heat. In 1847 Hermann von Helmholtz states the conservation of energy in general.

5. 1848

   An absolute scale. William Thomson, later Lord Kelvin, proposes a temperature scale that starts from an absolute zero and doesn’t depend on any particular substance. Its unit is now the kelvin.

6. 1865

   Entropy gets its name. Rudolf Clausius names the quantity S entropy, after the Greek word τροπή (tropē), which he glossed as Verwandlung, “transformation,” and he chose the word to sound like “energy.”

7. 1877

   Counting arrangements. Ludwig Boltzmann connects entropy to probability: the more ways the molecules can be arranged, the higher the entropy. Max Planck later wrote it as S = k log W, which is carved on Boltzmann’s tombstone in Vienna.

8. 1906

   Nernst’s heat theorem. Walther Nernst describes how entropy changes vanish as temperature approaches absolute zero, the beginning of the third law.

9. 1930s

   The zeroth law gets its number. Ralph Fowler suggests calling the most basic law, about equilibrium and temperature, the zeroth law, since the first three were already named.

10. 2019

    A constant fixed forever. The SI is redefined, and the Boltzmann constant is now exactly 1.380649 × 10⁻²³ J/K. The kelvin is defined from it, no longer from the properties of water.

Thermodynamics elsewhere on the site

Sources

• OpenStax University Physics Volume 2: 1.1 Temperature and Thermal Equilibrium, 1.4 Heat Transfer, Specific Heat, and Calorimetry, 2.2 Pressure, Temperature, and RMS Speed, 3.3 First Law of Thermodynamics, 4.2 Heat Engines, 4.3 Refrigerators and Heat Pumps, 4.5 The Carnot Cycle, 4.6 Entropy, 4.7 Entropy on a Microscopic Scale (including the third law)
• NIST: Kelvin: Boltzmann Constant
• NIST Guide to the SI, footnotes (the calorie and the kilocalorie)
• Popular Science Monthly (1877), History of the Dynamical Theory of Heat, on Wikisource (Rumford)
• APS News: James Prescott Joule and the Mechanical Equivalent of Heat
• Wikipedia (secondary): Timeline of thermodynamics, History of entropy, Entropy (Clausius’s 1865 footnote on τροπή), Boltzmann constant, Zeroth law of thermodynamics