Wither Heat Engines (part II)
The limits of civilization are thermodynamic
Famous science fiction author Arthur C. Clarke had a lot to say about predicting the future. He warned that the main flaw with predictions was a failure of imagination, going so far as to state in 1962 that advanced technology would appear to us as magical.
He was right and wrong in interesting ways. He himself imagined artificial general intelligence in the 1990’s and commercial fights to the moon in the 2000’s, which are both wrong but for different reasons. Golden age authors generally failed to foresee how computer technology would transform every part of our world by transducing intellectual products into digital forms. Lasers were relatively new in 1962, and although writers could easily imagine laser death rays, they could not conceive of laser printers.
As for spaceflight, they assumed it would follow the same trajectory as aviation: evolving from dangerous prototypes to commercial comfort in a matter of decades. That was wrong because of lack of power. The high-powered future of near-term science fiction never arrived.
As we saw in part I when it comes to power generation we’re still stuck in the 18th century. Our civilization is powered primarily by heat engines not fundamentally different from the first steam engines. Even atomic power plants have a steam engine at their heart.
The massive cooling towers needed for these plants are a monument to their inefficiency. Even modern turbines extract less than half the energy in hot steam. The remaining water is still hot and has to be cooled. The fuel spent to produce that heat is effectively wasted.
Every heat engine has to shed vast amounts of waste heat. Cars have radiators where up to 70 percent of the fuel energy in the gas tank is boiled off as worthless heat. Jets and rockets seem futuristic, but they just reject waste heat in their exhaust. Rocket engines in particular circulate cryogenic fuels to cool the hot combustion system, then burn the hot fuel and send that heat out the back as part of the rocket plume.
For the first time in centuries humanity is building, or trying to build, an entirely new energy system. It leverages the existing electric grid, but with photovoltaic cells for generation and batteries for off-grid usage. Response to the climate catastrophe will ironically result in a more efficient usage of energy and less waste heat.
It’s plausible to argue that solar cells have zero waste heat. Which isn’t to say they are efficient — they are not. But sunlight reaching the ground is going to heat the surface regardless, and whether or not plants or photocells capture some of that energy for later use doesn’t change that. The Earth’s solar energy flux is the same if we utilize it or not.
Electric systems are also vastly more efficient than the same systems driven by heat engines. Electric cars convert nearly 80% of the power from the grid into useful motion, and that includes charging and discharging the batteries. Gas engine cars have large radiators with powered fans and coolant pumps, evidenced on the front by a huge grimace of a grille. EV’s don’t have grilles, and many get by on passive cooling.
The solar punk vision of distributed generation networks and a low-friction electric grid, while significantly more efficient than burning carbon fuels, is nowhere near enough to support Clarkean “indistinguishable-from-magic” technology. I’m going to analyze just two such fictional technologies from a thermodynamic perspective.
Lightsaber
The laser swords of Star Wars don’t even seem that farfetched. Laser and plasma-based cutters are widely used today for cutting metal and other materials. The lightsaber is just the same thing but more compact.
In The Phantom Menace the heroes use a lightsaber to try to breech a bulkhead door. Qui Gon jams his blade through the door, which appears to be about 10cm thick, and starts to trace a hole about 1 meter in diameter. He only gets about halfway, taking about 10 seconds.
The ring of material being melted is a path 2cm wide on a 1 meter semicircle, and 10cm deep, which is about 300 cm³. At 8 grams per cm³, that’s about 2 kg of steel. It takes one megajoule of energy to melt a kilogram of steel, so this cut takes 2 MJ. Releasing 2 MJ in 10 seconds takes a power source capable of generating 200 kilowatts. By comparison, the most powerful handheld laser we can make today is 3 watts.
Suppose the sword masses 1 kg and has the same heat capacity as steel. If the power source is 90% efficient then it’s producing 200 kilojoules of heat. The handle of the sword will get 400 °C hotter in just the 10 seconds of cutting.
Impulse Engine
In Star Trek the ships have two types of propulsion: wrap drive for cruising between stars at thousands of times the speed of light, and impulse engines for movement in normal space. We can’t really say anything about how these drives function — even the normal-space engines don’t seem to consume reaction mass — but we can do calculations nonetheless.
In Star Trek: The Motion Picture there’s a sequence where the warp engines are disabled, and Captain Kirk orders Sulu to take a tour of the solar system on impulse alone. Some point later we cut back and find the Enterprise in the vicinity of Jupiter. Since they started at Earth the ship must have moved there, and by moving it acquired kinetic energy, and that energy came from the engines one way or another.
A low-energy Jupiter voyage takes 2 years, but that doesn’t fit with the plot. I’ll be generous and give them 8 hours to get the Enterprise from Earth to Jupiter, say 600 million kilometers. Using constant power they could accelerate the starship at 13 gees the whole way, arriving at Jupiter with a relative velocity of 3 million meters per second (1% the speed of light!).
The Enterprise mass is 2 million kilograms, so the kinetic energy is 2e6 kg x (3e6 m/s)² x ½ = 20,000,000 terajoules. That’s the equivalent of 10 kilograms of antimatter combining with the same amount of normal matter. Sulu’s joyride was burning over a kilo of antimatter per hour, generating one million terawatts. By comparison, the entire 21st century Earth generates a total of 2 terawatts.
These are astronomical numbers. Even if the engines were 99% efficient, then running the impulse drive would produce waste heat equivalent to a 1 megaton atomic bomb every second.
The reality of thermodynamics forecloses on the kinds of miraculous technologies we imagine in science fiction. Any time large amounts of energy are being put to work there will be proportionate losses as waste heat. Managing and dissipating that heat is the primary limit to how much power can be brought to bear on a problem.
That said, there is a joker is this deck: superconductivity. Room temperature superconductors could disrupt this picture considerably, but that’s a topic for another time.
