Heat moves from areas of higher temperature and low energy to areas of what?

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It seems your statement is backwards. To quote physics4kids.com:

Air mass of high pressure forces large numbers of molecules into areas of low pressure. Areas of high temperature give off energy to areas with lower temperature.

The correct observation in ordinary circumstances, then should be, "Heat moves from areas...

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It seems your statement is backwards. To quote physics4kids.com:

Air mass of high pressure forces large numbers of molecules into areas of low pressure. Areas of high temperature give off energy to areas with lower temperature.

The correct observation in ordinary circumstances, then should be, "Heat moves from areas of high temperature and areas of HIGH energy to areas of low temperature and low energy."

But, perhaps you are thinking of a material that is higher in energy in its natural state, such as a piece of firewood.  Then, you start a fire in the fireplace with this wood, give the wood some activation energy to get it combining with oxygen from the air (oxidation).  As the wood burns, it combines with the oxygen to produce ash, a product of the chemical reaction.  It also give off heat in the form of fire, which qualifies it as an exothermic reaction.  The resultant product when the fire has consumed the wood is a powdery white ash, hardly the solid wood product one started with.  Higher energy was given off as the chemical reaction progressed, resulting in a product with lower energy.  The trade was the emission of heat (exothermic) while the fir progressed.

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