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