is done when a moves something through a distance. To do work on the object, the force must act in the same direction as, or opposite the direction of, the object’s . Work can be positive or negative. In each energy system where work is done, you can think of work as the product of the prime mover and another . In mechanical systems, force is the prime mover. Work done on an object is the product of the applied force and the distance the object moves while the force is applied. If the system rotates, the applied force creates a . The work done on a rotating object is the product of the torque and the angle in radians through which the object rotates while the torque is applied. When the force is in the same direction as the object’s displacement, work is positive. When force is opposite the direction of displacement, work is negative. In fluid systems, pressure (or pressure difference) is the prime mover. A fluid can do work under constant pressure when the volume of fluid changes. In this case, work done by the fluid is the product of the pressure and the volume change. A fluid can also do work in steady flow. When the fluid density is constant, work done is the product of the pressure drop and the volume. When the fluid does work, work is positive. When work is done on the fluid, work is negative. In electrical systems, potential difference is the prime mover. Work is done on charge (electrons in electrical circuits) to move the charge through a potential difference. Work done is the product of potential difference and charge moved.

118 CHAPTER 2 WORK The table below summarizes the work equations in the three energy systems. Work is not done in thermal systems.

Energy Prime Work Units System Mover Equation SI English Mechanical

Translational Force W = F × d 1 J = 1 N • 1 m 1 ft • lb = 1 ft • 1 lb

Rotational Torque W = τ × θ = 1 N • m × Δ Fluid Pressure W = P V N 3 lb 3 1J=1• 1 m 1ft= 1• 1 ft m2 ft 2 or or Pressure

Difference W = –ΔP × V = 1 N • m

Electrical Potential W = ΔV × q 1 J = 1 V • l C

Difference = 1 V • C

CHAPTER 2 SUMMARY 119