Metal hot. Make food hot.

Think a bit deeper. How quickly is that heat transferred, and at what peak temperatures? Does the metal keep any heat of its own and impart that into the food, or does it just convey the heat from the burner to the food? And how quickly does it do that?

but my wife seems to think cast-iron is necessary for certain things (searing a prime rib roast, for example.).

Look at the thermal mechanics of this.

Take the cast iron pot. You can throw that on the stove and let it get ripping hot, like the metal itself is carrying a ton of heat energy. When you put the prime rib in it, the metal dumps its heat into the meat much faster than a flame alone would. This helps you get a strong sear on the outside, without dumping in too much total quantity of heat to cook the meat on the inside more than you want.

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then I gotta figure out gas vs. electric vs. induction vs infrared…

Heat can be transferred 3 ways- conduction (flows between two touching objects), convection (hot object heats air, air blows against cold object, air heats cold object) and radiation (hot object radiates energy through space and it warms cold object).

Electric- coils get hot, the pan touching the coils transfers heat by conduction. Downside is uneven heating- neither the pan nor the coils is perfectly flat so you get hot spots.

Infrared- coils under the glass get hot and radiate heat through the glass. This works pretty well.

Induction- coils under the glass but they don’t get hot. Instead they create a magnetic field modulated at low radio frequencies (15-150 KHz). This fluctuating magnetic field interacts with any ferrous metal close to it, creating small but powerful eddy currents inside the metal and thus heating the metal up. So the stove doesn’t create any heat at all, it’s the pan that actually gets hot. This by the way is neither conduction convection nor radiation, because heat isn’t being transferred, it’s created inside the pot.

Gas- flammable gas (usually propane or natural gas, which is mostly methane) burns creating high temperature exhaust gases that rise against the pot and thus heat the pot. Many chefs like this. Gas stoves should ideally be used with an overhead hood as gas stoves have been proven to drastically reduce indoor air quality.

Of the options- induction is usually the best these days, because it’s the most efficient, cleanest, and also in many cases has the highest output (in terms of watts of heat pumped into the pot).

When cooking, you want a stove capable of very high output. The more output you have, the faster it will boil water for example.