How to find internal energy with constant temperature?

AI Thread Summary
The discussion addresses the complexities of calculating heat transfer and internal energy in systems where temperature remains constant. It highlights that the heat formula Q=mc(T2-T1) is an approximation due to the variability of specific heat with temperature. There is confusion regarding the definitions of heat, with one emphasizing thermal energy transfer and the other focusing on energy stored within a system. The conversation raises the question of whether a single equation exists to calculate internal energy when temperature does not change. The need for clarity in these concepts is evident, particularly in educational contexts.
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since specific heat c changes with temperature, but its treated as a constant in the heat formula, so that means that heat formula Q=mc(T2-T1) is just an approximation? correct?

I see some texts define heat as Heat, q, is thermal energy transferred from a hotter system to a cooler system that are in contact.(from Khan Academy), and some texts define it as energy stored inside of something. from the heat formula, if there is no temperature change, then the heat is 0. So the second definition is incorrect?

do we have a single equation that calculates internal energy stored in a system with no temperature change, for example at a given instant of a bottle of water?
 
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