How to find internal energy with constant temperature?

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SUMMARY

The discussion centers on the concept of internal energy and the implications of using specific heat capacity (c) as a constant in the heat formula Q=mc(T2-T1). It is established that while the formula provides an approximation, it does not account for the variability of specific heat with temperature. The definitions of heat vary, with one emphasizing thermal energy transfer and the other focusing on energy stored within a system. The participants seek a definitive equation for calculating internal energy at constant temperature, particularly in scenarios where no temperature change occurs.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically internal energy and heat transfer.
  • Familiarity with the heat formula Q=mc(T2-T1) and its components.
  • Knowledge of specific heat capacity and its temperature dependence.
  • Basic concepts of thermal equilibrium and energy conservation.
NEXT STEPS
  • Research the relationship between specific heat capacity and temperature variations in different materials.
  • Explore the first law of thermodynamics and its application to internal energy calculations.
  • Study the concept of thermal energy transfer in systems at equilibrium.
  • Investigate advanced thermodynamic equations that account for internal energy changes without temperature variation.
USEFUL FOR

Students studying thermodynamics, physics educators, and professionals in engineering fields focusing on energy systems and thermal dynamics.

EastWindBreaks
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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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I just realized that I should post this in the homework section, I can't find the delete button for this post.
 

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