Is boiling actually necessary for this scenario? Let’s say the planet had pockets of pressurized gas instead. We drill into them, the gas expands, does work, and cools below ambient temperature.
This suggests Kelvin’s formulation is actually ok, if we focus on the word “by”. The work has to be extracted solely from cooling: something cools below the lowest temperature of surrounding objects, some work is extracted, and no other changes happen. If something else happens—for example a rock falls down, a spring is released, a container is depressurized, two fluids get mixed and so on—that doesn’t count.
Boiling is the mechanism that absorbs ambient heat and lets you extract useful work. It gives you a process that can run for quite a while, converting ambient heat into energy.
Think of a classical steam engine: a train could run a long distance on a single tank of water. But if the tank just held pressurized gas, you’d barely get anywhere. Boiling keeps the pressure going, since water expands to about 2000 times its initial volume as it turns into steam. That expansion is what lets you siphon off useful work from the environment.
(Yes, at first that phase change goes into pressure rather than volume, but once the steam is released into the atmosphere, the expansion ratio stand.)
Eventually, the process ends. Unlike a steam train, the water pocket on Planet X can’t be “retanked”. Once it’s gone, it’s gone. You’ve spent the initial structure. But in the meantime, the boiling phase change acts as a clever thermodynamic lever, allowing you to trade ambient heat for work far beyond a single burst.
Is boiling actually necessary for this scenario? Let’s say the planet had pockets of pressurized gas instead. We drill into them, the gas expands, does work, and cools below ambient temperature.
This suggests Kelvin’s formulation is actually ok, if we focus on the word “by”. The work has to be extracted solely from cooling: something cools below the lowest temperature of surrounding objects, some work is extracted, and no other changes happen. If something else happens—for example a rock falls down, a spring is released, a container is depressurized, two fluids get mixed and so on—that doesn’t count.
Boiling is the mechanism that absorbs ambient heat and lets you extract useful work. It gives you a process that can run for quite a while, converting ambient heat into energy.
Think of a classical steam engine: a train could run a long distance on a single tank of water. But if the tank just held pressurized gas, you’d barely get anywhere. Boiling keeps the pressure going, since water expands to about 2000 times its initial volume as it turns into steam. That expansion is what lets you siphon off useful work from the environment.
(Yes, at first that phase change goes into pressure rather than volume, but once the steam is released into the atmosphere, the expansion ratio stand.)
Eventually, the process ends. Unlike a steam train, the water pocket on Planet X can’t be “retanked”. Once it’s gone, it’s gone. You’ve spent the initial structure. But in the meantime, the boiling phase change acts as a clever thermodynamic lever, allowing you to trade ambient heat for work far beyond a single burst.