Why does a hot cup of coffee always cool to room temperature, while a lukewarm cup never heats itself up by drawing warmth from the air? Nothing in the law of conservation of energy forbids the second event; the energy would simply move the other way. The answer lies in one of the deepest ideas in science. It explains why engines can never be perfectly efficient, and why so many everyday processes run in only one direction.

What heat is

Until the nineteenth century most scientists thought heat was an invisible fluid called caloric, which flowed from hot bodies to cold ones. In 1798 Benjamin Thompson, known as Count Rumford, supervised the boring of cannon barrels in Munich. He noticed that the friction of the drill produced heat without any apparent limit, as long as the horses kept turning it. Rumford argued that the endless heat from boring cannon showed heat could not be a substance, but must be a kind of motion. Joule's measurements, described in the last level, completed the case.

We now understand that every substance is made of atoms and molecules in constant jiggling motion. Temperature is a measure of the average energy of motion of the particles in a substance. Heat is energy that flows from a hotter object to a cooler one because of their difference in temperature. The two are not the same: a bathtub of warm water holds more total thermal energy than a cup of boiling water, but the cup has the higher temperature, and heat will flow from the cup into the bath. The coldest possible temperature is absolute zero, about minus 273 degrees Celsius, the point at which particles have the least possible energy of motion. It can be approached very closely but never quite reached.

Three ways heat travels

Heat moves in three ways. Conduction is heat passing through direct contact, as faster particles jostle their neighbors: a metal spoon in hot soup warms all the way to the handle. Convection is heat carried along by a moving fluid such as air or water: warm air rises from a radiator and cooler air sinks to take its place. Radiation is heat carried by light and other electromagnetic waves, and it needs no material at all. That is how the Sun warms the Earth across empty space. A good vacuum flask blocks all three, with a vacuum gap against conduction and convection and a shiny lining against radiation.

The second law and entropy

In 1824 a young French engineer, Sadi Carnot, asked how much useful work a steam engine could possibly get from its fuel. He found that a heat engine works only by letting heat flow from a hot place to a cold one, and it must always release some of that heat to the cold side, no matter how well it is built. Rudolf Clausius in Germany and William Thomson, later Lord Kelvin, in Britain later built on his work. In 1850 Clausius stated what became the second law of thermodynamics: heat flows on its own only from hotter bodies to colder ones, never the reverse. A refrigerator does move heat from cold to hot, but only by using energy from the wall socket.

In 1865 Clausius coined the word entropy. Later Ludwig Boltzmann in Austria gave it a picture in terms of atoms. In his view, entropy measures how many ways the particles of a system can be arranged without changing its overall state; loosely, how spread out its energy is. There are vastly more ways for energy to be spread out than concentrated, so concentrated energy tends to spread, just as a well shuffled deck almost never falls back into perfect order. In an isolated system, total entropy tends to increase over time. This one-way tendency is often called the arrow of time: eggs break but do not unbreak. It also means that energy, though never destroyed, spreads out and becomes steadily less useful. Energy scattered as faint warmth in the air can no longer easily drive a machine.

Worked example: the car engine and the heat pump

A gasoline engine burns fuel at a high temperature and uses the hot gas to push pistons. Carnot's reasoning says it must dump much of that heat into the cooler surroundings, through the radiator and the exhaust pipe. In practice a typical car engine turns only around a quarter to a third of its fuel's energy into motion; the rest leaves as heat. An electric motor avoids this particular limit because it does not run on a temperature difference, which is one reason electric cars use energy more efficiently, though the power station that made the electricity may itself be a heat engine.

A heat pump runs the idea in reverse. Like a refrigerator turned inside out, it uses electricity to move heat from cold outdoor air into a warm house. Because it moves heat rather than making it, it can deliver around three units of heat for each unit of electricity it uses. This does not break conservation of energy: the extra comes from the outside air. A puzzle that looks like a free lunch turns out to be sound engineering, once the second law is understood.