What is temperature? Heat vs temperature and absolute zero

Temperature is a measure of how hot or cold something is, and physically it tracks the average energy of motion of the atoms and molecules inside it: the faster they jiggle, the higher the temperature. Heat is something different. It is energy moving from a hotter thing to a colder one because their temperatures differ. Temperature has a floor, absolute zero, at −273.15 °C, but no known ceiling.

In short

• Temperature is about the average energy per particle; heat is energy in transit, flowing from hot to cold.
• A big thing at a modest temperature can hold far more heat energy than a small thing that is much hotter.
• Absolute zero, 0 K, is where particles have the least energy they can have. It can be approached ever more closely but never reached.

What is temperature, physically?

Everything is made of particles that never stop moving. In a gas they fly about and collide; in a liquid they tumble past each other; in a solid they vibrate in place. Temperature measures how vigorous that motion is. In a gas, it is directly proportional to the average kinetic energy, the energy of motion, of the molecules. At 20 °C, the nitrogen molecules that make up most of the air move at about 511 meters a second on average, as OpenStax's physics text works out, faster than a jet airliner, each one changing direction billions of times a second as it collides.

A thermometer works because two objects in contact trade energy until their temperatures are equal, a state called thermal equilibrium. Put a thermometer in your mouth and it warms until it matches you; then it reports its own temperature, which is now yours.

"Average energy of motion" is a good picture, not the full definition. In solids and liquids part of the energy is stored in the stretching of bonds, and quantum mechanics says particles keep some motion even at absolute zero. Physicists define temperature more generally through entropy: the less a system's entropy grows when a little energy is added, the higher its temperature. That definition covers every case, and it is also why heat always flows from hot to cold.

What is the difference between heat and temperature?

Temperature is a property of an object; heat is energy on the move between objects. Something doesn't contain heat the way it contains mass. It contains internal energy, the total energy of all its particles, and heat is the part of that energy that crosses from one object to another because of a temperature difference. Heat is measured in joules, like any form of energy; temperature in kelvins or degrees.

The amount of heat it takes to warm something is Q = m × c × ΔT. Q is the heat in joules, m is the mass in kilograms, c is the specific heat capacity of the material, and ΔT is the change in temperature. Water's specific heat is about 4,186 joules per kilogram per degree: it takes 4,186 J to warm 1 kg of water by 1 °C, which is a lot compared with most materials, and why the sea warms and cools slowly.

A worked example: a bathtub against a cup of boiling water

Compare a 250 mL cup of water at 100 °C with a bathtub of 150 liters at 40 °C, in a room at 20 °C. How much heat does each give off as it cools to room temperature? A liter of water has a mass of about 1 kg.

• The cup: Q = 0.25 kg × 4,186 J/kg°C × (100 − 20) °C = 83,720 J, about 84 kilojoules.
• The bath: Q = 150 kg × 4,186 J/kg°C × (40 − 20) °C = 12,558,000 J, about 12.6 megajoules.

The cup is much hotter, but the bath gives off about 150 times more heat, enough to warm the bathroom noticeably, while the cup barely changes the room. Temperature says how concentrated the energy is in each particle; how much heat flows depends also on how many particles there are.

The same idea explains a sauna. Air at 90 °C is bearable for a few minutes, but water at 90 °C scalds instantly. Air is thin and carries little energy per liter, and it passes heat to skin slowly. Water is dense, holds far more energy, and transfers it fast.

How do you convert Celsius, Fahrenheit and kelvin?

Three scales are in common use. Celsius sets water's freezing point at 0 and boiling point at 100, at sea-level pressure. Fahrenheit, from 1724, puts them at 32 and 212. Kelvin, the scientific unit, uses degrees the same size as Celsius but starts at absolute zero, so it has no negative numbers and is written without the degree sign.

Point	Kelvin	Celsius	Fahrenheit
Absolute zero	0 K	−273.15 °C	−459.67 °F
Water freezes	273.15 K	0 °C	32 °F
Normal body temperature, about	310 K	37 °C	98.6 °F
Water boils, at sea level	373.15 K	100 °C	212 °F

The formulas are °F = °C × 9/5 + 32, °C = (°F − 32) × 5/9, and K = °C + 273.15. Two worked conversions:

1. A 25 °C day: 25 × 9/5 = 45, plus 32 = 77 °F. In kelvin, 25 + 273.15 = 298.15 K.
2. An oven at 350 °F: 350 − 32 = 318, times 5/9 = 176.7 °C, or about 450 K.

The scales cross at one point: −40 °C is exactly −40 °F. Anders Celsius's original scale of 1742 ran the other way, with 0 for boiling and 100 for freezing; Carl Linnaeus and others flipped it around the time of Celsius's death in 1744.

Since 20 May 2019, the kelvin has been defined by fixing the Boltzmann constant, which links a particle's energy to temperature, at exactly 1.380649 × 10⁻²³ joules per kelvin, as NIST explains. Before that, it was pinned to the triple point of water, where ice, liquid water and vapor coexist at 273.16 K.

What is absolute zero, and why can't it be reached?

Absolute zero is 0 K, −273.15 °C: the temperature at which a system has the lowest energy it can have. It was first inferred from gases. Cool a gas at constant volume and its pressure falls in a straight line; extend the line and it hits zero pressure at about −273 °C, everywhere and for every gas.

It cannot be reached. The third law of thermodynamics implies that each cooling step can lower the temperature only by a fraction of what remains, so getting all the way to zero would take infinitely many steps. What labs can do is get extremely close: laser cooling and related tricks have produced gases at less than a billionth of a kelvin. At those temperatures atoms can merge into a single quantum state, a Bose–Einstein condensate. Even a few kelvin is cold enough for some metals to lose all electrical resistance.

Even at absolute zero, particles would not be perfectly still. Quantum mechanics leaves them a minimum jiggle, called zero-point energy. Absolute zero means the least motion possible, not none.

Deep space is not at absolute zero either. The faint afterglow of the Big Bang fills the universe at about 2.7 K, a floor that anything in space not heated by a star settles toward.

What do people get wrong about temperature?

The most common mistake is treating heat and temperature as the same thing, which the bathtub example corrects. A second is thinking cold is a substance that flows. A cold metal bench feels colder than a wooden one at the same temperature because metal conducts heat away from your skin faster, not because it holds more "cold". Your skin senses heat flow, not temperature, which makes it a poor thermometer.

A third is assuming adding heat always raises the temperature. When ice melts or water boils, heat goes into breaking the bonds between molecules, and the temperature holds steady until the change is complete; this is why a pot of boiling water stays at about 100 °C however high the flame. Those changes between solid, liquid and gas are covered in the states of matter. The body, meanwhile, works hard to hold its own temperature near 37 °C, one of the clearest cases of homeostasis.

Check yourself

• Without looking back: why does a bath at 40 °C give off more heat than a cup of boiling water?
• Explain why a metal bench feels colder than a wooden one beside it, though both are at the same temperature.
• What would it take to reach absolute zero, and why does that make it impossible?

Sources

• Kelvin: Introduction — National Institute of Standards and Technology
• Absolute zero — Wikipedia
• 1.4 Heat Transfer, Specific Heat, and Calorimetry, in University Physics Volume 2 — OpenStax, Rice University
• Celsius — Wikipedia
• 2.2 Pressure, Temperature, and RMS Speed, in University Physics Volume 2 — OpenStax, Rice University
• 1.5 Phase Changes, in University Physics Volume 2 — OpenStax, Rice University