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The internal energy of a system is identified with the random, disordered motion of molecules; the total (internal) energy in a system includes potential and kinetic energy. This is contrast to external energy which is a function of the sample with respect to the outside environment (e.g. kinetic energy if the sample is moving or potential energy if the sample is at a height from the ground etc). The symbol for Internal Energy Change is\( ΔU\).
One gram of water at zero °Celsius compared with one gram of copper at zero °Celsius do NOT have the same internal energy because even though their kinetic energies are equal, water has a much higher potential energy causing its internal energy to be much greater than the copper's internal energy.
ΔU = q+w
where q is heat and w is work
An isolated system cannot exchange heat or work with its surroundings making the change in internal energy equal to zero.
ΔUisolated system = 0
Energy is Conserved
ΔUsystem = -ΔUsurroundings
The signs of internal energy