Along this line, I was thinking about the use of areothermal power on mars by circulating water in a closed loop system then using the geysering effect to bring heat and energy the surface (taking power using hydraulic ram). But the challenges of insulating drill-pipe on earth make steaming oil reservoirs much below 500 meters uneconomic (implies technologically uncompetitive for now). On Mars the added complications would be far worse. Water freezes too easily. {snip}
Where's the math?Unless you have some plausible numbers for the heat transfer, and the amount of mass required on Mars to produce a specific power level, it seems a bit pointless.More than likely, solar cells and batteries (for night time) would produce more continuous kW per kg.
The important thing is not the working fluid or the phase changes involved but the amount of heat available in the Martian crust. Until this is known it is impossible to say if useful power could be generated.
Theoretical estimates of the thermal gradient within the Martian crust are good and fine, but until it is actually measured this form of power generation is not a given.