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: translational kinetic energy vibrational and rotational kinetic energy potential energy from intermolecular forces Example 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. ΔU isolated system = 0 Energy is Conserved ΔU system = - ΔU surroundings 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 Δ U isolated system = 0, ΔU system = -ΔU surroundings 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 Outside Links Levine, Ira N. "Thermodynamic internal energy of an ideal gas of rigid rotors." J. Chem. Educ. 1985 : 62, 53.