Heat and temperature
Classical physics can be pictured as standing on three pillars: mechanics, electromagnetism, and the science of heat. Courses 3 and 4 followed the first two. The third drove the first industrial revolution, since the steam engine is a machine for turning heat into work. It also brought new ideas into physics, ideas that turned out to be deeper, simpler, and more beautiful than anything before.
There are two ways to study heat. Classical thermodynamics measures the large-scale quantities anyone can feel: a pot of water’s temperature, or how much heat flows when cold water is poured in. Statistical thermodynamics looks down at the molecules, far too many to follow one by one with Newton’s laws. Only Laplace’s demon could do that. Instead it treats them by probability, with astonishingly good results. This lesson starts with the first approach.
People have known fire since before history. China remembers the sage Suiren, who taught humanity to make fire by drilling wood. Greece remembers Prometheus, who stole fire from the gods. Yet for a very long time, people couldn’t tell heat from temperature. Hot meant a lot of heat; cold meant little. The confusion held back the whole subject.
Measurement began with, once again, Galileo. Around 1593 he made a thermoscope: a glass bulb of air above a column of water. Warm the bulb in your hand and the air expands, pushing the water down. It had no scale and wasn’t accurate, but it was the first time anyone could see temperature change. By the 1760s the Scottish chemist Joseph Black had drawn the key distinction. Temperature is how hot something is. Heat is how much warmth it takes in or gives off, and melting ice, for example, absorbs heat without getting any warmer.
In the 1780s the French chemist Antoine Lavoisier and the mathematician Pierre-Simon Laplace, Newton’s great admirer from Course 4, built an ingenious ice calorimeter. It had three layers. The outer layer, packed with ice, kept out the heat of the room. The middle layer also held ice, with a drain at the bottom. The inner chamber held whatever was being studied, perhaps a hot potato. Heat from the object melted ice in the middle layer, and the water that drained out measured how much heat had been given off.
Step by step, concepts like temperature, heat, pressure, volume, and specific heat were pinned down. One principle underlies all of them, and later physicists called it the zeroth law of thermodynamics: two bodies in thermal equilibrium with each other have the same temperature. It sounds too obvious to need saying, but without it no thermometer could be trusted. A thermometer reads its own temperature. Only because it comes into equilibrium with your body does it tell you yours.
The caloric fluid
What is heat? The favored answer around 1800 was caloric, an invisible, weightless fluid that flows from hot bodies to cold ones like water running downhill. Lavoisier even listed caloric among the chemical elements. When you touch something hot, the caloric flows into you.
Then came a cannon. In 1798 Count Rumford was supervising the boring of cannon barrels at the arsenal in Munich, and noticed how hot the metal became. Where was all that heat coming from? He set up a careful test. A blunt borer turned inside a brass cylinder weighing more than a hundred pounds, with no heat supplied from outside. In half an hour the cylinder warmed from about 16°C to about 55°C, while the borer scraped off only about 54 grams of metal. If all that heat had been squeezed out of the chips, they would have had to reach thousands of degrees. They didn’t. And the heat kept coming as long as the boring went on.
Something that can be produced without limit, Rumford argued, can’t be a stored fluid. Heat must be a kind of motion, the motion of the particles inside the metal.
Joule’s paddle wheel
The Englishman James Prescott Joule (1818–1889), a brewer’s son from Manchester, turned that idea into numbers. Today the unit of energy bears his name. The physicists who matter most get units named after them: the newton, the ampere, the joule.
In the 1840s Joule hung weights from cords wound around an axle. As the weights fell, the axle turned a set of paddles inside an insulated container of water. The paddles churned the water, and its temperature rose. No heat went in from outside. The only thing that went in was the work of the falling weights. Joule measured the tiny temperature rise with great care and found a fixed exchange rate between work and heat. In today’s units, one kilocalorie of heat equals about 4,184 joules of work.
You already know one such exchange. A swinging pendulum trades height for speed and speed for height: potential energy becomes kinetic energy and back again. Joule showed that mechanical energy can also become heat, at a fixed rate, and nothing is lost along the way.
Follow the energy
A ball rolls back and forth in a bowl. Watch its energy change form, then add friction and see where the “lost” energy goes.
The total never changes. Friction doesn’t destroy energy; it turns the ball’s motion into the random motion of molecules, which we feel as heat.
One law for every kind of energy
Physicists always want the most universal rule. Mechanical energy turns into heat. What about the energy of living things? Lavoisier and Laplace had already put a guinea pig into their ice calorimeter in the early 1780s. They measured the ice it melted and the carbon dioxide it breathed out, and found that an animal’s warmth matches, roughly, what burning the same amount of carbon would release. Life, they concluded, is a slow combustion. Later experiments, with better insulation and precise measurement of the oxygen consumed and carbon dioxide produced, confirmed that biological energy and heat are the same currency. Electricity joined the list too: run a current through a wire in water, and the heat the water gains matches the electrical energy used.
Together these results became the first law of thermodynamics: heat can pass from one body to another, and can turn into mechanical or other forms of energy and back, but in every conversion the total stays the same. Physicists then generalized it into one of the most basic laws of nature, the conservation of energy. Energy is never created and never destroyed. It only changes form.
It is manifestly absurd to suppose that the powers with which God has endowed matter can be destroyed any more than that they can be created by man’s agency.
James Prescott Joule, lecture in Manchester, 1847
There is a neat twist. Two of the law’s discoverers came from medicine. Julius Robert Mayer, a German ship’s doctor, noticed on a voyage to Java in 1840 that sailors’ blood from their veins was unusually bright red in the tropics. He reasoned that in hot weather the body burns less fuel to keep warm, and that food, heat, and work must be equivalent. Hermann von Helmholtz, who gave the law its general form in 1847, trained as a physician. You could say that if physics gave biology the microscope, biology repaid physics with the conservation of energy.
Why did Rumford’s cannon-boring experiment count against the caloric theory?
Closer to home
Every Calorie on an American food label traces back to this lesson. In the 1890s the chemist Wilbur Atwater built a room-sized respiration calorimeter at Wesleyan University in Connecticut. Volunteers lived in it for days while Atwater measured everything they ate, the heat they gave off, and the gases they breathed. The energy in their food matched the energy that came out, which showed that conservation of energy holds for human beings too. His measurements gave nutrition its familiar rule of thumb: about 4 Calories per gram of protein or carbohydrate and 9 per gram of fat. The Calorie on a label, with a capital C, is a kilocalorie, about 4,184 of Joule’s joules.
Another view
The story usually credits Mayer, Joule, and Helmholtz, but in a famous 1959 essay the historian Thomas Kuhn counted about a dozen people who reached some version of energy conservation between 1830 and 1850, often independently. Kuhn called it a case of simultaneous discovery. Engineers studying engines, physicians studying bodies, and philosophers seeking unity in nature all converged on it. And the law itself kept growing. Einstein’s E = mc² showed that mass is also a form of energy, so what is conserved is mass and energy together.
What to keep
- Temperature and heat are different: temperature is how hot something is, heat is energy flowing because of a temperature difference.
- Rumford’s cannon and Joule’s paddle wheel showed that heat is a form of motion, and that work turns into heat at a fixed rate.
- Mechanical, thermal, biological, chemical, and electrical energy all convert into one another. The total never changes: conservation of energy.
Think it over
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Sources and further reading
- Benjamin Thompson, Count Rumford, “An Inquiry concerning the Source of the Heat Which Is Excited by Friction,” Philosophical Transactions of the Royal Society 88, 1798.
- Hasok Chang, Inventing Temperature: Measurement and Scientific Progress, Oxford University Press, 2004.
- Thomas S. Kuhn, “Energy Conservation as an Example of Simultaneous Discovery,” in Critical Problems in the History of Science, ed. Marshall Clagett, University of Wisconsin Press, 1959.
- Crosbie Smith, The Science of Energy, University of Chicago Press, 1998.