When volume and temperature are kept constant, shouldn't internal energy remain constant (as it's a state function depending on state variables)? When heat is supplied, why does the internal energy increase if state variables are kept constant?
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3 Answers
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For a system likely to be the seat of a chemical reaction, the variables of state are not limited to the temperature and the volume: it is necessary to add the extent of reaction.
answered Dec 5, 2021 at 8:29
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The relation that you are using for total internal energy change is only half the picture, the first law of thermodynamics relates total internal energy change to heat supplied -work done by the body, remember that heat is nothing but energy in flow. Also, work done is not a state function, remember that if the pressure is not constant, then a gas CAN and WILL do work by expanding and contracting back to the original volume (that is why we integrate with respect to volume, it's the area under a P-V graph that matters, not the initial volume). If temperature and volume are constant, it is the pressure that is changing. I assume there must be a discussion in the text you are reading about this topic, after the routine isobar and adiabatic cases.
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Internal energy comprises of both the potential energy and the kinetic energy. So when heat is applied, Kinetic energy would inevitably increase unless the matter is at its melting or boiling point. As kinetic energy increases, and internal energy = potential energy + kinetic energy, total internal energy increases too.
