Stupid question: can we harness this 100 year old heat to power something today?

You can't exactly harness heat; what can be harnessed is a temperature differential, to convert into some form of mechanical motion or electrical potential. You'd need some apparatus that connects the hot mass and some cold sink with thermocouples. Whether that's possible or feasible on the scale of the London Tube, I don't know.

https://en.wikipedia.org/wiki/Thermoelectric_effect

Instead of that, probably a more feasible way to make use of heat is just as heat, by some way of circulating it into buildings in the winter. One interesting angle of looking at this would be that it's really an artificially created geothermal source.

An additional dumb question. If all the expense was undertaken to build all the piping to functionally turn the tube into a heat source for buildings, how long would it take to sap the stored heat from the soil to the point where the temperature differential doesn't work anymore? At some point would they have to switch from having it be a heat source in winter to making it a heat dump in summer?

Heat is energy, so I find it surprising that it can't be harnessed. Is it really not possible to take some of the energy out of a system and use it for something?

Not all heat is useful. If there was a magic device that could take any heat and convert it into electricity, global warming could be trivially reversed.

There is the Seebeck effect, where you run a Peltier junction in reverse. Efficiency is, to put it mildly, low. [1]

[1] https://en.wikipedia.org/wiki/Thermoelectric_generator

This still works from a temperature differential, not just a quantity of heat.

furthermore you could prevent the heat death of the universe :)

Air conditioning is really silly when you think about it. It takes a ton of energy to move some energy outside. It feels like it could be self powered.

It's actually forcing the energy apart. The energy wants make this one big mess where every bit is the same temperature as every other bit.

Your AC is working hard at pushing all the heat outdoors and making a pocket of cool inside.

Self-powered evaporative air conditioning is an ancient technology.

Air conditioning as we understand and use it today is a gold-plated band-aid over bad design. It's so entrenched you almost can't get a house built any other way.

If it got hot enough you could use a geothermal-type generator for reasonable efficiency, but that is (of course) still exploiting a temprature differential (a place where water remains liquid, and a hot place where it becomes high pressure steam to drive a turbine). However sadly that is unlikely to happen before the tunnels become unlivable :)

Yes

https://www.newcivilengineer.com/innovative-thinking/harness...

Pump cold air down, suck warmer air up, heat buildings in winter. Same idea lots of passive houses use to regulate temperature.