Heatcapacity C defines the relationship between the heat absorbed ΔQ and the temperature change ΔT: C = ΔQ/ΔT. Specific heat capacity c is normalized per kilogram of substance. Gases, liquids, and solids differ by orders of magnitude. Monatomic gas (argon) has a molar heat capacity of about 12.5 J/(mol·K), diatomic oxygen — 20.8 J/(mol·K), and crystals — approximately 25 J/(mol·K) (Dulong–Petit law). Water breaks records: 4.2 kJ/(kg·K), twice as high as one might expect — colossal energy goes into overcoming hydrogen bonds between molecules. That is precisely why tea cools in a quarter of an hour, while milk — in five minutes.
History
Joseph Black in the 1760s, studying the heat of fusion of ice, noticed that different bodies require different amounts of 'fire' for the same heating, and called this 'capacity for heat'. Dulong and Petit in 1819 formulated the empirical law of constant atomic heat capacity (~6 cal/(mol·K)). Ludwig Boltzmann in 1871 gave the first statistical explanation via equipartition of energy among degrees of freedom. Albert Einstein in 1907 applied the quantum hypothesis to atomic vibrations in a crystal, and Peter Debye in 1912 refined the theory by accounting for the full spectrum of phonon modes. Today, heat capacity measurements are a standard tool for investigating phase transitions, superconductivity, and topological materials.
How it works
Statistical mechanics connects heatcapacity with fluctuations of internal energy: C_V = (⟨U²⟩ - ⟨U⟩²)/(k_B T²). In a classical ideal gas, C_V = (f/2)R, where f is the number of quadratic degrees of freedom. Debye model: C_V = 9R (T/θ_D)³ ∫_0^{θ_D/T} (x⁴ e^x)/(e^x-1)² dx. For metals, the contribution of the degenerate electron gas is significant: C_el = (π²/2)(k_B²/g(ε_F)) T, which at low temperatures becomes C_V = γT + βT³ — a formula used to determine the density of states at the Fermi level and the Debye temperature. Magnetic materials exhibit heat capacity peaks at magnetic transitions (λ-anomalies). In glasses and amorphous solids, an excess low-temperature heat capacity is observed due to tunneling two-level systems. The heat capacity of a black hole, computed by Bekenstein and Hawking, is negative (in the sense of stability).
In practice
The high heatcapacity of water moderates the climate: oceans accumulate daytime heat and release it at night. In engineering, the low heat capacity of copper allows radiators to quickly dissipate heat.
Fun fact
If the oceans had the heatcapacity of sand, at night the planet would freeze down to minus one hundred degrees, and during the day it would heat up to plus one hundred.
At the center of nearly every large galaxy sits a supermassive black hole. It doesn't just devour infalling gas; it also blasts some of it back out in powerful jets. These jets act like giant pistons, shoving the surrounding gas and heating it. Astronomers have long suspected that this is how black holes keep galaxies from cooling into cold star factories.
One universal interpreter for all dialects of sodium. Liquid sodium in a reactor behaves differently: near the pipe wall it is dense and fast, near the boiling surface it is rarefied and slow. Previously, each state required its own set of calculations, as if hiring a new translator for every phrase.
Swimming season opens when the water feels tolerable. But everyone has their own threshold: one person shivers at twenty degrees, another swims comfortably at fifteen. Scientists decided to figure out where this difference comes from.
They compared a swimmer's body to a house trying to keep heat in while a cold wind blows outside.
A regular battery releases heat smoothly: what you store is what you get. The power is fixed once and for all, like a faucet that pours water in a single stream. But sometimes you don't need a steady flow; you need a short, powerful burst: to instantly heat a part, trigger a reaction, or dump excess heat.
A regular battery releases heat smoothly: what you store is what you get. The power is fixed once and for all, like a faucet that pours water in a single stream. But sometimes you don't need a steady flow; you need a short, powerful burst: to instantly heat a part, trigger a reaction, or dump excess heat.
A billiard ball hangs in midair. Tiny peas shoot at it from a blowgun. Each hit is barely perceptible, but if the ball is very light and barely trembles from heat, you can make out individual nudges. That's essentially the setup: a glass sphere the size of a bacterium levitates in a vacuum while a narrow beam of xenon atoms flies at it.
Inside an MRI magnet, current flows through a closed superconducting loop, like water circling in a bucket after you give it a spin, it just keeps going on its own. To change that current, you heat the loop with a small heater: it stops being superconducting, becomes an ordinary resistor, and then an external source can 'top up' or 'draw off' current.
A translator who has memorized all the lines in advance responds instantly — no need to listen to the whole conversation again. That's how the new model works: instead of running atoms through a computer for hours, it immediately outputs the crystal's free energy at any temperature and pressure.
A translator who has memorized all the lines in advance responds instantly — no need to listen to the whole conversation again. That's how the new model works: instead of running atoms through a computer for hours, it immediately outputs the crystal's free energy at any temperature and pressure.
Hot water after a shower, warm air from ventilation, the heated walls of an engine — all this is heat below 100°C. Usually, it dissipates without doing any useful work. Now it can be captured and turned into electricity.
Inside the new device is a wire made of a nickel-titanium alloy. This material remembers its shape: when heated, it contracts; when cooled, it returns to its original shape.
A conventional computer computes by shuttling electric charges along wires. But can you compute with heat? A network of pipes carrying hot and cold water can perform simple logic operations if the pipes are connected in the right order.
A microchip the size of a fingernail gives off as much heat as a small light bulb. Getting rid of that heat is like trying to cool a cup of hot tea with a teaspoon: the insulating material around transistors is usually a poor heat conductor.
A conventional computer computes by shuttling electric charges along wires. But can you compute with heat? A network of pipes carrying hot and cold water can perform simple logic operations if the pipes are connected in the right order.
A light field, like a neat waffle iron, presses a regular pattern of bright and dark regions into space. Atoms get stuck in the brightest spots as if in tiny dimples: that's an optical lattice. It's a favorite tool for physicists who want to study quantum behavior of matter in its pure form.
It all started with stretching. In the first fractions of a second, the universe ballooned — physicists call this inflation. Then the rapid expansion gave way to a phase where the field's energy converted into ordinary particles.
In an oven, as temperature rises, molecules move faster and disorder increases. With language models like ChatGPT, it's the opposite. When developers increase the 'temperature' parameter, the model gets access to a wider choice of words, but its long texts suddenly start looping.
A team of researchers tested 11 different AIs by generating 12,000 text continuations.
In a glass of water, oil gathers into droplets: that's equilibrium separation dictated by chemistry. But there are systems where order arises not from rest but from a constant flow of energy.
Any battery, from a AA to a quantum one, is simple in principle: there's a store of energy, and there's a way to get it out. In the quantum world, this 'way' looks like a careful switching between particle states, akin to moving a ball from a high shelf to a low one.
In classical thermodynamics, heat engines are like a virtuoso musician on stage: the closer to perfection in performance (Carnot efficiency), the slower the tempo (power).
Imagine water as a ballroom, where each molecule is a dancer, constantly forming fleeting partnerships. These hydrogen bonds give rise to local patterns: some resemble a stiff waltz — an ordered network with cavities (low-density structure), others a wild jitterbug, where partners crowd into chaotic dense clusters.
The Mpemba effect is a mystery where hot вода sometimes freezes faster than warm water. Usually this is attributed to how вода loses heat and энтропию (a measure of disorder). But in a glass of water, chaos prevents a precise model.
Physicists built a quantum model: a particle in a well with two depressions separated by a barrier.
Water is not just a wet substance. On a picosecond scale, it resembles a dance floor where molecules continuously break and form bonds with each other. Usually, this dance is described by one main movement — collective relaxation, as if the whole crowd simultaneously slows down after the music stops.
When physicists drive electrons through an ultrapure gallium arsenide channel at helium temperatures, they expect to see a well-behaved, almost ideal fluid.
The void is never truly empty. In curved spacetime (for instance, in an expanding universe or near a black hole) the vacuum heats up. This is reminiscent of how acceleration makes particles appear seemingly out of nowhere: a phenomenon known as thermal vacuum radiation.
In a hot mug, water sometimes freezes faster than in a warm one. This paradox is over half a century old and is called the Mpemba effect. It is usually attributed to fluid motion or evaporation. Now physicists have shown that a similar trick is possible without water, just through radiation of heat.
A glass of hot tea sometimes cools faster than a glass of warm tea. This paradox, known as the Mpemba effect, was long considered a curiosity from the world of liquids. But physicists have found it where no one expected: in the faint glow of organic films placed in a magnetic field.
A well-coordinated orchestra of electrons in a superconductor is easily thrown off rhythm. Thermal jolts destroy the fragile order, and resistance returns. For decades, scientists have sought ways to strengthen this ensemble — mostly by changing the material's composition or compressing it to unimaginable pressures.
Press a piece of tape against glass: it holds firmly, but run a warm finger over it, and the film lifts off on its own, leaving no marks. That's exactly how the new material behaves, made from liquid crystal elastomers — polymers whose molecules are arranged like a liquid crystal.
If you squeeze water between two glass plates so that only two layers of molecules fit, it becomes something between a liquid and ice. At room temperature, molecules in such a trap still move but arrange themselves into a semblance of a crystal lattice.
An ordinary black hole is like a stove that heats up more as its mass shrinks. A tiny hole should glow at unimaginable temperatures and evaporate in an instant. But that scenario ignores quantum corrections — what happens when the very fabric of spacetime begins to tremble.
Imagine a slide with three dips: the deepest one is a stable position for a ball, the middle one is precarious. A slight push and the ball rolls down. Yet, constant vibration of the right strength can hold it in the middle hollow for a long time.
In the 1950s, physicists Lee and Yang discovered that all states of matter are separated by invisible points in the world of imaginary numbers.
Tea in a cup cools quietly on the table. But if you zoom past at near-light speed, the thermometer will read higher — even though no one heated the tea. Calculations confirm: the needle will creep up.
A century ago, physicists split into three camps.
Two white sheets lie in the sun — one rough, one smooth. Which one heats up less? The rough one scatters light more strongly, so it seems it would stay cooler. But if the coating is made of many transparent glass beads, the logic changes. Light wanders through it like in a thick fog, and at some point it stops noticing individual droplets.
An ordinary battery in a phone stores energy in chemical bonds — slowly, with heat and wear. A quantum capacitor works differently: it charges not with matter but with rhythm. A swing that is pushed in time with its motion accumulates energy in the motion itself, without friction.
A pot of water on the stove eventually settles down: the temperature evens out, the liquid stops boiling. Physicists call this thermal equilibrium — a state where energy is distributed in the most probable way.
A pot of water on the stove: the hotter the burner, the faster ice turns to water, and water to steam. Heat destroys order. But sometimes nature pulls a trick, and heating makes a liquid freeze, like a puddle turning to ice on a frosty morning.
A thin crack runs through glass. At first glance, the fracture line simply reflects the material's brittleness. But if you zoom in to the atomic level, the picture gets more complex: glass starts to resist differently when the crack accelerates.
A hot spoon in a cup of tea — heat runs along the metal from the hot end to the cold one. Textbooks describe this process as atoms jiggling and passing on their jolts to each other. But atoms don't just jiggle: they also spin, like tiny tops. Until now, physicists had no common language to describe both motions at once.
The authors of the work built such a language.
A gold speck the size of a hundred atoms catches a beam of light, and heats up. In everyday life, that's no big deal, but in the world of nanotechnology, this tiny heat can ruin a biosensor or fry a microchip. You can't just put a fan on it: at these scales, heat gets trapped like in a thick winter coat.
An ordinary flash drive in your pocket gets warm even when it's just sitting there. Now imagine memory that, in the cold, uses almost nothing, like a thermos that never cools down. A superconductor carries current without loss at liquid-helium temperatures, but it couldn't store data. The new cell changes that.