Developing a Mathematical Representation for Thermal Phenomena
If nothing lost to the ‘environment’ all the heat lost by the hot water is gained by the cold water:
heat energy lost by hot water = heat energy gained by cold water
If some heat energy goes into the environment:
Heat energy lost by hot water = heat gained by cold water + heat gained by environment
Conservation of heat energy:
energy lost = energy gained
Think of amount of energy transferred as depending upon how much “stuff” you have, what kind of ‘stuff it is, and how much the temperature changed.
How do we express that idea mathematically?
(how much stuff)(property of that stuff)(how much temperature changed):
(Mass of water)(how much energy is needed to change the temperature of one gram by one degree)(how many degrees the temperature changed)
Water is a standard, so we define a calorie of heat energy in terms of water: Need one calorie of heat energy to change the temperature of one gram of water by one degree Celsius. Hot water: (Mass of hot water)(1 calorie/ gram degree)(change in temperature of hot water) = heat lost Cold water: (Mass of cold water (1 calorie/ gram degree)(change in temperature of cold water) = heat gained by cold water + any heat lost to the environment Conservation of energy: heat lost = heat gained
This is the justification for an algebraic equation representing heat transfer when mix hot and cold water:
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What if want to know how much hot water:
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