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= ²P. The work done by the gas when the volume expands from volume V₁ to volume V₂ is - 1² PC W = PdV. In a steam engine the pressure and volume of steam satisfy the equation PV14=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/in² and a volume of 500 in³ and expands to a volume of 1300 in³. (Round your answer to two decimal places.) W = ft-lb piston head"

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