When the surroundings do work on the system, the internal energy of the system becomes larger, so E is positive. The relationship between the magnitude of the work done by a system when it expands and the change in the volume of the system was previously described by the following equation. The figure above shows that the sign convention for work of expansion can be included by writing this equation as follows. When equations connect two or more properties that describe the state of the system, they are called equations of state . The ideal gas law, for example, is an equation of state.
Temperature is a state function.
No matter how many times we heat, cool, expand, compress, or otherwise change the system, the net change in the temperature only depends on the initial and final states of the system. The same can be said for the volume, pressure, and the number of moles of gas in the sample. These quantities are all state functions. Heat and work are not state functions. Work can't be a state function because it is proportional to the distance an object is moved, which depends on the path used to go from the initial to the final state.