Consider an ideal gas contained in a piston–cylinder arrangement as a closed thermodynamic system. The gas expands following a polytropic process PVⁿ = P₁Vn₁ from state 1 to state 2. The polytropic exponent n is a constant.

A. Starting with the definition of moving-boundary work ∫ Pdv derive an
expression to evaluate the work in terms of the pressures and volumes at the  initial and final states.

B. Is the work for this process into or out of the system? Why?