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Can a solar thermal collector common on private roofs today designed for collecting heat for the household ever collect enough heat to power a stirling engine of say this model:

Normally a stirling engine of this model is powered by combustion of natural gas.

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A solar thermal collector is not really the best choice to power a stirling engine. Usually a solution consisting mainly of water is used in these collectors and temperatures only go up to about 120°C. So they are great to provide warm water and heat but not electricity, as the conversion efficiency is inherently low if the temperature difference is not very high.

Much better suited is a solar furnace (wiki) which can reach temperature above thousand degrees Celsius. While small devices exists for cooking in sunny climates the larger ones use mirrors that follow the movement of the sun and I have not heard of a small household version. Technically it's possible, but economically probably not as you need a large area to put up all those mirrors.

In general is the efficiency of every thermal engine is limited by the Carnot efficiency $$\eta = 1 - \frac{T_{cold}}{T_{warm}}$$ For small temperature differences the efficiency drops rapidly.

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