Whilst the price per kWh of the various energy sources are of course important, but the way the energy is converted in to heat and its applied to the substance you want to heat is also very important.
With Gas rings (Nat Gas or LPG) to maximise heating efficiency you should carefully match the size of the flame to size of the pan. Having the fame turned up too high means there is an increasing amount of gas used that is effectively wasted as it pass up the sides of the pan/kettle. There will always be some hot bypass gasses which means efficency is low.
Similarly with Halogen and the earliest coiled contact elements, if you can see any of the halogen light or the contact surface of element, that mean heat produced in those visible areas is wasted.
Induction hobs react to the presence of the magnetisable base of a saucepan, and the energy is concentrated to it, so its less wasteful than almost any other system.
Just as an indicator, if you heat a pan of water, on an induction hob, you will see water vapour rising above the pan well before it actually boils. Put te same pan on a gas ring, and you will barely see any water vapour until its boiling. The reason is with an induction hob, the heat is only entering through the reaction of the pans bas to the hobs emitter, and there is very little warm air rising around the pan. This means the air around the top of the pan remains considerably cooler which allows water vapour to form into its visible phase much sooner.
Gas hobs have so much hot exhaust gas bypass that the air around the sids and above the pan is much warmer, which does two things, it increases the airflow velocity above the pan diluting any water vapour, and its heating it which prevents the water vapour from condensing into visible vapour so early.
The inefficiencies of high exhaust bypass from gas rings, and to slightly lesser extent of halogen and electric rings when using under sized pans, might well change the overall cost effectiveness of all the energy sources by quite a lot.
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