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When gas expands in a cylinder with radius r, the pressure P at any given time...

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 = πr2P. The work done by the gas when the volume expands from volume V1 to volume V2 is

W =

V2 P dV
V1

.

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 done by the engine during a cycle when the steam starts at a pressure of 160 lb/in2 and a volume of 500 in3 and expands to a volume of 1100 in3. (Round your answer to two decimal places.)

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