In a Steam Engine the Pressure and Volume of Steam $P V ^ { 1.4 } = k$

In a steam engine the pressure and volume of steam satisfy the equation $P V ^ { 1.4 } = k$ , 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 (in $\mathrm { ft } - \mathrm { lb }$ ) during a cycle when the steam starts at a pressure of $160 \mathrm { lb } / \mathrm { in } ^ { 2 }$ and a volume of $100 \mathrm { in } ^ { 3 }$ and expands to a volume of $1000 \mathrm { in } ^ { 3 }$ . Use the fact that the work done by the gas when the volume expands from $V _ { 1 }$ to volume $V _ { 2 }$ is
$W = \int _ { V _ { 1 } } ^ { V _ { 2 } } P d V$