When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the volume V: P = P(V). The force exerted by the gas on the piston (see the figure) is the product of the pressure and the area: F = pr2P. The work done by the gas when the volume expands from volume V1 to volume V2 is W.

In a steam engine the pressure and volume of steam satisfy the equation PV1.4 = k, where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Calculate the work W done by the engine during a cycle when the steam starts at a pressure of 120 lb/in2 and a volume of 300 in3 and expands to a volume of 800 in3. (Round your answer to three significant digits.)
W = ft-lb