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 = TTI'ZP. The work done by the gas when the volume expands from volume V1 to volume V2 is V2 W =/ PdV- V1 In a steam engine the pressure and volume of steam satisfy the equation PVl'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 done by the engine during a cycle when the steam starts at a pressure of 120 lb/inZ and a volume of 500 in3 and expands to a volume of 900 in3. (Round your answer to two decimal places.) mm piston head