I don't understand what high and low efficiency means in this context and how it applies to the environment. All electric stoves convert electricity to heat; do you mean to say that natural gas is the better environmental choice? Please correct me if I'm misunderstanding you.
It is hard to use clear terminology without getting very technical. The basic idea is that a gas power station has a limited efficiency, I think about 55% of the chemical energy in the gas becomes electrical energy. This is due to a mixture of engineering limitations and fundamental thermodynamic limits of a heat engine (http://en.wikipedia.org/wiki/Heat_engine#Efficiency).
So for gas hobs to beat induction hobs, if we assume 100% efficiency for an induction hob (electrical energy to heat energy in the food), the pan needs to get >55% of the chemical energy from the gas into the food.
I don't have any figures but it isn't infeasible that a gas hob could be more efficient.
Gas is certainly more efficient. And every time local fire departments get called out for CO alarms or gas smells, I'm reminded why I had the gas line on the house I bought disconnected anyway.
Electricity is usually generated by turning heat into motion, which is then turned into electricity. You lose energy at each stage, but the heat to motion stage is limited by Carnot's Theorem, which puts an upper bound on the efficiency of heat engines. Efficiency varies based on implementation, but it almost never rises above 50%.
If you need heat, it's much more fuel efficient to just burn fuel and not bother turning it into electricity in an intermediate step.
"If you need heat, it's much more fuel efficient to just burn fuel and not bother turning it into electricity in an intermediate step."
This isn't always true. Carnot's Theorem works in reverse as well, so you can use a heat pump (like an air con unit) so get more heat out of your electricity than just dumping it into a coil. This is actually practical and is being done today for heating houses, you can easily beat the other inefficiencies because the temperature difference that you are trying to create for your house is much smaller than the one between the gas furnace and the ambient temperature around the power station.
For heating a pan though I think this is unlikely to be practical any time soon.
However, it's extremely inefficient to move that heat from a burner to a pot by just sticking the pot above the burner. It's much more efficient to, say, heat your house by burning stuff locally than it is to use electricity, but the heat transfer losses are huge for flames and cookware, so induction wins out.
Efficiency varies based on implementation, but it almost never rises above 50%.
"According to the U.S. Department of Energy, the efficiency of energy transfer for an induction cooker is 84%, versus 74% for a smooth-top non-induction electrical unit, for an approximate 10% saving in energy for the same amount of heat transfer.[20]" -- http://en.wikipedia.org/wiki/Induction_cooking#Efficiency_an...
I advise caution about various percents being thrown around without enough context. I understood the 50% figure above as describing the conversion of heat energy into motion, e.g. inside of a natural gas power plant. The figures you quote are defined as being on the customer side of the energy meter.
Further below that calculation is updated to try and reflect the source fuels using some US EPA numbers: "The (US averaged) inefficiencies recalculated relative to source fuels energies are hence 25% for induction cooking surfaces using grid electricity, 84% for induction cooking surfaces using on-Site Solar, and 38% for gas burners.
The original point (that burning fuel to heat things to spin things to make electricity which is moved to your home to heat a pan is less efficient than moving the fuel to your home and burning it there to heat a pan) is maybe better illustrated by the EPA source-site ratios given to make that adjustment: "3.34 for electricity purchased from the grid, 1.0 for on-site solar, and 1.047 for natural gas. The natural gas figure is slightly greater than 1 and mainly accounts for distribution losses". So if the "electricity purchased from the grid" was generated with natural gas in the first place, you can and see the difference there.
