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In a Steam Engine the Pressure and Volume of Steam PV1/4=kP V ^ { 1 / 4 } = k

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In a steam engine the pressure and volume of steam satisfy the equation PV1/4=kP V ^ { 1 / 4 } = k , where kk 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 (in ft-lb) during a cycle when the steam starts at a pressure of 160lb/in2160 \mathrm { lb } / \mathrm { in } ^ { 2 } and a volume of 100in3100 \mathrm { in } ^ { 3 } and expands to a volume of 1000in31000 \mathrm { in } ^ { 3 } . Use the fact that the work done by the gas when the volume expands from V1V _ { 1 } to volume V2V _ { 2 } is
W=V1V2PdVW = \int _ { V _ { 1 } } ^ { V _ { 2 } } P d V

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