Scales, Absolute Zero, and What a Thermometer Really Does

Three things from last time

• Your hand does not measure temperature — it measures how fast energy leaves your finger.
• "Being in thermal equilibrium with" is an equivalence relation: reflexive, symmetric, and transitive — the transitive part is the Zeroth Law.
• Temperature is the name of an equivalence class. Two systems have the same temperature exactly when they are in the same class.

One sentence for the whole term

• Temperature is a STATE quantity — a property a system has right now, like mass or volume.
• Heat is a PROCESS quantity — it only exists while energy is being transferred because of a temperature difference. Once the transfer stops, there is no more "heat" to speak of.
• What the body actually has, at any instant, is internal energy — the total energy of all its particles.

The Celsius scale: two fixed points

0 °C

melting ice

100 °C

boiling water

How cold can something actually get?

• The steps between temperatures are equal (50 °C each time). Look at how the volume changes each step.
• If this pattern kept going in a straight line — no phase changes, nothing weird — at what temperature would the volume reach zero?
• You don't need graph paper for a first estimate. Work with your neighbour.

Whatever gas you use, the line always crosses zero at the same point

Stop and answer this before we move on

• If your answer is "because that's the rule", the concept has not landed yet.
• The real answer: Kelvin is built ON TOP OF the physical fact that there is a coldest possible state. The scale doesn't forbid negative numbers — reality does.

Three real, measured phenomena

• Superconductivity — some materials lose ALL electrical resistance. A current started in a loop of superconducting wire can keep flowing, essentially forever, with nothing lost as heat.
• Superfluidity — liquid helium flows with zero viscosity. It can climb up and over the wall of its own container, against gravity, just to reach a lower level outside.
• Bose–Einstein condensate — cool a cloud of atoms enough and they lose their individual identity, merging into one single giant quantum wave, as if they were one atom.

It depends what you mean by "place"

• Coldest large, human-built region we know of: CERN's Large Hadron Collider, 1.9 K (−271.3 °C) — colder than the vacuum of outer space itself (2.7 K, the leftover glow of the Big Bang).
• Colder still, but natural and 5,000 light-years away: the Boomerang Nebula, about 1 K — gas expanding so fast it cools itself down.
• Colder than either, but only in a speck a few atoms wide: laboratory experiments have reached temperatures thousands of times closer to zero than deep space.

No — and the reason is more interesting than the myth

• The myth pictures 0 K as "all motion completely stops." That part is already false.
• Quantum mechanics (Heisenberg's uncertainty principle) guarantees a tiny irreducible motion even at 0 K, called zero-point energy. A particle can never be perfectly still AND perfectly located at the same time.
• Time itself isn't a thermal quantity — it doesn't slow because something got cold. What actually grinds to a halt near 0 K is chemistry: reactions become so slow they might as well not happen.

Two conversions, worked together

• Room temperature, about 20 °C → 20 + 273 = 293 K
• Liquid nitrogen boils at 77 K → 77 − 273 = −196 °C

The Fahrenheit scale: which two points, exactly?

• Later scientists fixed 32 °F and 212 °F as the two official reference points, exactly 180 degrees apart — body temperature then had to be recalculated to 98.6 °F.
• Still the everyday scale in the United States and a handful of other places.

Celsius and Fahrenheit were never the only two

Predict, before we build the vocabulary for it

In the very first second or two, what does the liquid column do?

• Rises steadily from the start
• Stays still, then rises
• Drops slightly, then rises
• Oscillates up and down before settling

Three words you'll need on 18 September

Calibration

Fixing the scale using two known points (0 °C and 100 °C) and marking equal divisions in between.

Sensitivity

How much the reading changes for a given change in temperature. A narrower tube means higher sensitivity.

Range

The minimum and maximum temperature the instrument can actually read.

Back to the cold thermometer

• The GLASS bulb touches the hot water first, and glass is thin — it warms and expands almost immediately.
• That sudden expansion of the glass makes room INSIDE the bulb before the liquid itself has had time to warm up. The liquid drops slightly to fill the extra space.
• Only after that does the liquid itself heat through and expand — and it expands more per degree than the glass does, so it overtakes the glass and the column rises past where it started.

Six ways to build a thermometer

• Liquid-in-glass — expansion of a liquid's volume (mercury, alcohol)
• Bimetallic strip — two metals expand by different amounts, so the strip bends
• Resistance thermometer / thermistor — electrical resistance of a conductor or semiconductor changes
• Thermocouple — a voltage appears at the junction of two different metals (ovens, furnaces)
• Gas thermometer — pressure or volume of a gas at fixed conditions — literally the method used earlier today to find absolute zero
• Liquid crystal — a material changes colour at different temperatures (forehead strips)

The thermometer that never touches anything

• What it measures: infrared radiation. Every object warmer than absolute zero constantly gives it off — invisible to your eyes, but completely real.
• How it works: a lens focuses the incoming infrared onto a detector, which turns it into an electrical signal and calculates a temperature from it.
• The laser dot is NOT the measurement. It only shows roughly where the invisible measuring spot is aimed.

Think, then talk to your neighbour

• Two systems are placed in contact and, after a while, nothing more changes between them. What word describes this, and what quantity has actually become equal?
• Name a physical property — other than the height of a liquid column — that changes with temperature and could, in principle, be used to build a different kind of thermometer.
• You pour boiling water into a cup that was sitting at room temperature. What decides the final temperature they settle at together? Which law guarantees they end up at exactly the same temperature?

What temperature corresponds to 0 K?

1. −273 °C
2. 0 °C
3. 100 °C
4. It depends on the substance

A patient's body temperature is 37 °C. What is this in kelvin?

1. 37 K
2. 236 K
3. 310 K
4. 373 K

Why is there no such thing as −50 K?

1. The Kelvin scale starts at absolute zero, the lowest possible temperature
2. Thermometers simply cannot display negative Kelvin readings
3. It is a convention that nobody has ever changed
4. Negative Kelvin would be too cold to measure safely

Two identical metal blocks, one hot and one cold, are placed in contact and left until nothing changes. What do we now know for certain?

1. They have the same internal energy
2. They have the same temperature
3. They have both stopped emitting any energy
4. The hot block has transferred all its heat to the cold one

A thermometer is calibrated using ice water (0 °C) and boiling water (100 °C). Why two points, and not just one?

1. One point can only fix the origin — two points are needed to fix equal intervals in between
2. Two points show the maximum and minimum the instrument can read
3. Two points reveal how precisely the scale can be read
4. One point is never accurate enough on its own

For next time

• The open question has no single "correct" sentence — I am reading for whether you keep the two ideas separate.
• Next lesson, 15 September: thermal expansion — your first measurement with a visible error.