where U is internal energy, P is pressure, and V is volume. Under the conditions of a Joule–Thomson expansion, the change in P V represents the work done by the fluid (see the proof below). If P V increases, with H constant, then U must decrease as a result of the fluid doing work on its surroundings. This produces a decrease in temperature and results in a positive Joule–Thomson coefficient. Conversely, a decrease in P V means that work is done on the fluid and the internal energy increases. If the increase in kinetic energy exceeds the increase in potential energy, there will be an increase in the temperature of the fluid and the Joule–Thomson coefficient will be negative.