It might be more efficient to just compress air into the cylinders and use the compressed air to power the generator. A heat pump uses a compressor anyway, so we would eliminate a step by storing the compressed gas directly.

True, but I was hoping to use the heat-side for water boiling during the day, and then the cold-side for pressure & non-water boiling later, at night. This feels like it might be another perpetual motion scheme where I try to use the same energy twice, but I'm not sure.

If you're compressing it to get a phase-change you really will be able to store considerably more energy in a small spot. The phase change is a step function. Getting that energy back out is a challenge though.

I want to have a liquid that will boil if we just allow it to warm up to night-time natural temperatures. So we use solar generated electricity, which should become plentiful in the next 10 years, to lower the temperature for our mystery gas so it becomes a liquid... chilled to around zero Celsius.

So, yes... getting the energy back out is the key. We have to do better than batteries, which are also bad.

I've seen water pumped to a height so it can flow back down later... but that is very inefficient. What other methods are available to "store" energy for future use?

Chilling something during the day and heating it at night is working counter to the natural temperature change. The air normally is warmer during the day and cooler at night, which makes it logical to warm something during the day and use the naturally cooler air at night to produce a greater energy gradient.

Sort of... we have energy available during the day, how can we save some for night time use?

Take something that is a gas at warm temperatures, then cool it to make it liquid, keep it under pressure & a bit cool... then we can just let it warm up at night to get the phase change to drive the steam engine.

Steam, but not from water vapor.

Can we do better than using batteries? I admit "night time cold boiling" is not a fantastic return on the energy used during the day... but is it more efficient that out other options?

I'm having trouble making this clear, I'm just not sure how to explain the problem. Solar energy is (will be) great, but not at night. Do we just keep burning coal?

Well, it just seems to me that cooling something during the day when the air is naturally warmer and allowing it to warm up at night when the air is naturally cooler is not very efficient. Compressed air doesn't depend on warming or cooling so the day/night temp change won't matter as much.

It's true that the cooled/compressed gas would take up less space in liquid form, but you would still have to retain the gas after it is evaporated in order to reuse it. This would require a very large container. By contrast, if you just compress air during the day and use it to generate electricity at night, you would need a larger tank for the compressed air (due to it staying a gas) but you wouldn't need to store the unpressurized gas at all. It's in the unpressurized state that the gas will have the greatest volume. In other words, the compressed air tank would be far smaller than the combination of a small high-pressure tank plus a huge low-pressure tank.

Don't get me wrong. I think you idea is clever and it could possibly work. I just doubt that it would be as efficient as other methods.

BTW, another option already used for energy storage is to pump water upward (to a tank or reservoir) and then use it to generate electricity in a conventional hydroelectric generator. Normally, this is done large scale, but a small, household system might be workable to.

BTW, other options include flywheels and hydrogen fuelcells. There is also still the battery option, which really isn't all that bad.

Efficiency is everything. The current methods all have huge percentage losses. If cold boiling cannot do better, then there is no point. Its true that re-capturing the steam would take a lot of space, but then, by definition, solar takes a lot of space so this will not be a "down town" high-rent location.

This would work best if we use a liquid whose boiling point is near the night-time average/low temperature so that the day time cooling does not have far to go.

If you want efficiency, many batteries are extremely efficient. Flywheels are a little less efficient, but are still much more efficient than a steam engine powered generator. Really, efficiency isn't everything, cost and durability are equally important. If your idea has any really advantage, it would have to be in the cost and durability.

http://en.wikipedia.org/wiki/Grid_energy_storage

... Battery storage was used in the early days of direct-current electric power networks, and is appearing again. Battery systems connected to large solid-state converters have been used to stabilize power distribution networks. For example in Puerto Rico a system with a capacity of 20 megawatts for 15 minutes is used to stabilize the frequency of electric power produced on the island. A 27 megawatt 15 minute nickel-cadmium battery bank was installed at Anchorage Alaska in 2003 to stabilize voltage at the end of a long transmission line.[7] Many "off-the-grid" domestic systems rely on battery storage, but storing large amounts of electricity in batteries or by other electrical means has not yet been put to general use.

Batteries are generally expensive, have high maintenance, and have limited lifespans. ...

(There are potential innovations that could make batteries more effective)

Exactly. Like I said, batteries are efficient, but efficiency isn't everything. Batteries are not so great in their cost and durability. If your idea has merit, it is in the cost and durability, not efficiency.