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An Entire Lake Is Heated By Water From A Hot Spring At The Bottom Of The Lake, This Is Transfered By Convection, Radiation, Or Conduction?

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All of those would be present. Only an extremely small amount of heat would be transferred by radiation.  However, the actual heat transfer to the lake as a whole would be the result of both convection and conduction.  In most cases, we would think of the overwhelming amount of heat being moved most rapidly throughout the lake as a whole being convection- the actual physical movement/mixing of  the "hot" spring water.  However, the individual "hot" water molecules would also distribute their energy very rapidly to all the surrounding lower-temperature water molecules by conduction.  My answer would be that for a typical spring, the heat is transferred fairly widely and rapidly  throughout the lake by convection, but that same heat is also transferred throughout the lake's molecules by conduction.

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