In a steam engine the pressure P and the volume V of steam satisfy the equation P(V^1.4)=k, where k is a constant. This is true for adiabatic expansion, an expansion in which there is no heat transfer between the cylinder and its surroundings. How do you calculate the work done by the engine during a cycle when the steam starts at a pressure of 160lb/(in^2) and a volume of 100in^3 and expands to a volume of 800in^3?

Question

In a steam engine the pressure P and the volume V of steam satisfy the equation P(V^1.4)=k, where k is a constant. This is true for adiabatic expansion, an expansion in which there is no heat transfer between the cylinder and its surroundings.  How do you calculate the work done by the engine during a cycle when the steam starts at a pressure of 160lb/(in^2) and a volume of 100in^3 and expands to a volume of 800in^3?