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ChemWiki: The Dynamic Chemistry Hypertext > Core > Physical Chemistry > Thermodynamics > State Functions > Internal Energy

Internal Energy

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\( ΔU\).

Energy on a smaller scale

  • Internal energy includes energy on a microscopic scale
  • It is the sum of all the microscopic energies such as:
    1. translational kinetic energy
    2. vibrational and rotational kinetic energy
    3. potential energy from intermolecular forces



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.

Internal Energy Change Equations

The first law of thermodynamics

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

Ryan's chem wiki.jpg

ΔUsystem = -ΔUsurroundings

The signs of internal energy

  • Energy entering the system is POSITIVE (+), meaning heat is absorbed, q>0. Work is thus done on the system, w>0
  • Energy leaving the system is NEGATIVE (-), meaning heat is given off by the system, q<0 and work is done by the system, w<0
  • Since ΔUisolated system = 0, ΔUsystem = -ΔUsurroundings and energy is conserved.

Quick Notes

  • A system contains ONLY internal Energy
  • a system does NOT contain energy in the form of heat or work
  • Heat and work only exist during a change in the system
  • Internal energy is a state function


  • Lorraine Alborzfar (UCD)

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Last modified
08:19, 5 Dec 2013


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This material is based upon work supported by the National Science Foundation under Grant Numbers 1246120, 1525057, and 1413739.

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