Quantifying Work

Recall that a system’s internal energy is defined as the sum of heat and work. Heat is measured using calorimetry, but how is work quantified?

Work is the result of a force, which an object experiences – such as by being pulled, pushed, or lifted – over a distance. Thus work equals force times distance.

If a golf club hits a ball 100 feet, then it has done work. Energy is transferred from the club to the ball.

In this case, the ball is the system on which work is performed by the surroundings.

In chemical reactions, work can be associated with multiple physical or chemical changes in a system. A commonly encountered type of work is pressure-volume work.

Consider the combustion in an engine’s cylinder. Not only does the combustion generate heat, it also produces gas, which performs work.

When the gas volume in the cylinder expands, the pressure pushes the piston downward acting against external forces in the surroundings.

Pressure is defined as a force acting over an area. Here, the force from the expanding gases is distributed over the area of the base of the piston. In other words, the force is pressure times area.

Thus, work, which is force times distance, can be rewritten as pressure multiplied by the area and distance over which it acts. For the engine cylinder, this is the height difference the piston moves.

Considering that area times height is the volume of a cylinder, the equation for work can be defined as pressure times the volume change of the system.

However, because the volume increases and the piston is pushed downward, the system actually performs work on the surroundings, which by convention is a negative value.

Therefore, work is defined as the negative of the pressure, P, times delta-V or the change in final and initial volume, which happened during the expansion.

The unit for pressure-volume work is usually defined as liter-atmosphere. This unit can be converted to the conventional unit of energy, Joules, by using the conversion factor one liter-atmosphere is equal to 101.3 Joules.