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It would depend on the material, and how many degrees of temperature increase you are looking for. The specific heat of a substance is the exact amount of energy required to heat a specific mass by a certain number of degrees. For example, 1kg of water requires 4.186kJ of energy to raise it's temperature by 1 degree celsius. So if you know what material you have, and it's density, you can determine the mass of 1 cubic meter of it. Use the mass and the desired temperature increase, as well as the specific heat of that substance, and you can find out the energy required. Kilowatts are units of power, which is energy per unit time. So once you have the total amount of energy you need, divide by the amount of time you want the heating to occur, and you will have the total power requirement. So for water, heating 1kg by 1 degree celcius in 1 second requires 4.186kW of power.

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Q: How many kilowatts are neccery to heat 1 m cub?
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