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CalculusQ&A LibraryWhen 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 = v1 ꭍ v2 P dV 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 140 lb/in2 and a volume of 500 in3 and expands to a volume of 900 in3. (Round your answer to two decimal places.) W = _________________ ft-lbQuestion

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 = πr ^{2}P*. The work done by the gas when the volume expands from volume V

*W* = _{ v1} ꭍ ^{v2 } P dV

In a steam engine the pressure and volume of steam satisfy the equation PV^{1.4} = *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 140 lb/in^{2} and a volume of 500 in^{3} and expands to a volume of 900 in^{3}. (Round your answer to two decimal places.) W = _________________ ft-lb

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