OT: Electricity from Gas in your home

No. Energy is one of those things that gets conserved.

The problem is that to obtain mechanical work you need a heat source and a heat sink and maximum theoretical efficiency of a perfect ideal heat engine is determined by the difference of the two temperatures.

Fuel cell conversion of gas directly into electricity and hot water as a byproduct is quite doable. The electricity generated is around half the input gas content and the rest dumped into water as waste heat.

They are popular in Japan and Korea. Main snag is that the fuel cell catalyst can get poisoned too easily on mains gas.

It is ideal as a domestic combined heat and power system iff you have the right sort of gas.

Except you 'lose the energy' at the point of use not up the chimney stack miles away, the waste heat is very close to where it could be used for much of the year for hot water / space heating, possibly with the use of a heat pump to take advantage of the low grade of heat.

The electricity production costs are low if you ignore the fuel cell capital costs. A domestic supply of gas is around 2.5p/kWh, with a claimed 50% conversion efficiency in the fuel cell, results in an electricity production cost (on a fuel only basis) of 5p/kWh, so around 100% cheaper than normal retail.