Much less than using virgin materials. For example, recycling aluminum reduces energy use by 96%, compared to using virgin ore.
It depends on the material and how much of it you want to recycle. Essentially, one just needs to melt it down completely and then let it cool into a new shape. You can figure out how much energy it takes to recycle a particular mass of a particular material by looking up its specific heat and melting point. The specific heat is how much energy it takes to raise one gram of the material by one degree Celsius (different units can also be used for non-metric calculations). For water, the substance on which the metric system is based, it takes 1 calorie (4.18 joules) of energy to raise one gram by one one degree Celsius.
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