Heat, Energy and Engines: The Laws of Thermodynamics

Temperature and absolute zero

In the scene the particles of a gas jitter in a box; make it hotter and they move faster. Temperature measures the average energy of that motion. The mean kinetic energy of a gas molecule is E = 3/2·k·T, where k = 1.381 × 10⁻²³ J/K and T is the temperature in kelvin, K = °C + 273.15. At 20 °C, T = 293.15 K and E = 1.5 × 1.381 × 10⁻²³ × 293.15 ≈ 6.1 × 10⁻²¹ J. A nitrogen molecule at that energy moves at about 510 m/s. Nothing can be colder than absolute zero, 0 K or −273.15 °C.

Three roads for heat

A hot cup in a cool room loses heat until both match; it never flows back by itself. It travels in three ways. Conduction passes motion from particle to particle in a solid. Convection carries heat in a moving fluid, as warm air rises from a radiator. Radiation carries heat as light, even across empty space, which is how the Sun warms the Earth. For conduction, P = k·A·ΔT / d. If the faces of a 4 mm pane of glass (k = 1.0 W/(m·K), 1.5 m²) really differed by 20 K, it would pass 1.0 × 1.5 × 20 / 0.004 = 7,500 W. Real faces are almost equal, because still air does the insulating.

Two laws

The first law says energy is conserved: the change in internal energy is the heat added minus the work done, ΔU = Q − W. In the 1840s James Joule showed that paddles stirring water warm it by a measured amount for each unit of work. The second law says heat does not flow from cold to hot by itself, and no engine turns all the heat it takes in into work; some must go to something colder. An engine takes in 1,000 J, does 300 J of work and must reject 700 J, since 300 + 700 = 1,000. Its efficiency is 300 / 1,000 = 30 percent.

Four strokes

The cutaway shows one cylinder of a petrol engine. Intake: the piston goes down and draws in air and fuel. Compression: the piston rises and squeezes the mixture. Power: a spark ignites it, hot gas expands and shoves the piston down. Exhaust: the piston rises again and pushes the burnt gas out. Nikolaus Otto built the first successful four-stroke engine in 1876. The cycle takes two turns of the crankshaft, so at 3,000 revolutions per minute each cylinder fires 1,500 times a minute, or 25 times every second.

The Carnot ceiling

Even a perfect heat engine is limited. Sadi Carnot's result, in 1824, is efficiency = 1 − T_c / T_h, where T_h is the temperature of the hot source and T_c of the cold one, both in kelvin. With T_h = 800 K and T_c = 300 K the limit is 1 − 300 / 800 = 0.625, or 62.5 percent. Raise the hot side or cool the cold side and the limit rises. In the sandbox set both temperatures and watch the ceiling move; real engines always land below it because of friction and leaking heat.

Petrol against electric

A petrol engine in everyday driving turns about 25 to 30 percent of the fuel's energy into motion. A litre of petrol holds about 34 MJ, which is 34 / 3.6 ≈ 9.4 kWh; at 27 percent about 2.5 kWh reaches the wheels. An electric motor is not a heat engine, so no Carnot limit applies, and it turns about 90 percent of the electricity into motion. The power station and the battery have their own losses, but over a whole trip the electric car still wastes far less energy as heat.

Heat, energy and engines