Which is more efficient, heating water in microwave or electric stove? So our propane tank in the kitchen ran out again today.
Which is more energy efficient, boiling water in a microwave on an electric stove?  All things being equal i.e. starting temperature and mass of water.
Not so much about which is faster, but which will cost us less kWh generally.
I realize boiling from the stove noticeably heats up the environment as well, and continues emitting warmth long after its power had been switched off.  Does the kettle have a higher thermal capacity than the micro-safe glass container (therefore needing to absorb more calories) or is that difference negligible with say 1kg of water?  Haven't been inside a microwave to feel its thermal capacity/overhead though.
As far as dominant conduction/convection/radiation methods of transfer, it seems fairly obvious in both cases.
 A: According to http://en.wikipedia.org/wiki/Microwave_oven#Heating_efficiency the efficiency of a microwave oven is about 66%, and essentially all the microswave energy will be absorbed by the water so you get an overall efficiency of 66%.
I don't know what the efficiency of heating a pan on an electric hob is. There must be losses due to convection, but I couldn't begin to guess how much they reduce the overall efficiency of the stove. It will depend on all sorts of environmental factors.
It would be an easy and interesting experiment to do, as long as you have some way of measuring how much power your stove is drawing. Sadly I have a gas stove so I can't do the experiment myself. My dedication to experimental physics doesn't stretch to buying a new stove :-)
A: Looks like Ron Maimon is right, and the efficiency is pretty much the same for a microwave oven and an electric stove. There are some results of an actual comparison  for boiling a cup of water (the method does not look very accurate though, and the models used are old) at http://michaelbluejay.com/electricity/cooking.html : 0.087 kWh for a microwave oven vs. 0.095 kWh for an electric stove. Furthermore, energy used for cooking does not make a large part of your energy bills anyway (http://www.aceee.org/consumer/cooking : "If you don’t cook much, more efficient cooking appliances won’t save much energy!").
A: Greenest and cheap method is gas cooktop as it uses the primary energy, evethough the heating efficiency is low compared to others. Nest option would be microwave as it heats up only water. Next option would be an electric kettle as it has low  heatloss. Induction cooktop is also good option. Never use electric cooktop.
A: Again, heating of 1 litre of water from 20oC 100oC need 330kJ (0.091kWh) of heat. All these method provide the this amount of heat to water. If you look the kettle which will have about 90% effciency, require 0.183kWh of electricty. Mircowave has about 66% effciency requires 0.139 kWhr of electricity. The natural gas cook to has about 50% efficency, so they require 660kJ(0.183kWh). But cost wise the order is different. For Adelaide tarrif rates, gas is coming as chepaest with 1 cent where as 3.4 and 4.7 cents for kettle and microwave.  If you look at the CO2 emission, it can be estimated as 33, 88 and 112 grams of CO2 for gas and kettle and microwave.
In total, Gas is the winner, runner-up is kettle.
Stop, another challenger, Inducction cookop... may come 2nd... not winner!!
