Final answer:
A polytropic process in a steam piston-cylinder assembly is described by P * V^k = constant, where P is pressure, V is volume, and k is the polytropic index. Work done during the process can be calculated using the equation W = (P2 * V2 - P1 * V1) / (1 - k).
Step-by-step explanation:
In a steam piston-cylinder assembly, a polytropic process refers to a process in which the pressure-volume relationship of the steam is described by the equation P * V^k = constant, where P is the pressure, V is the volume, and k is the polytropic index. The polytropic index is a measure of how the pressure and volume change during the process. It is often represented by the ratio of specific heats, γ, for steam, which is approximately 1.3.
During a polytropic process, the steam undergoes work and heat exchange with the surroundings. The work done by or on the steam can be calculated by the equation:
W = (P2 * V2 - P1 * V1) / (1 - k)
where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and k is the polytropic index.