this is a THERMODYNAMICS problem

3. We will learn about multi-stage compression in this course. In multi-stage compression, the initial and final pressures are fixed, while the mid-stage pressure is a variable. We will derive the following relation for work done (W) in a multi-stage compressor. w (* [C%)*-114 [0 KRT k-1 KRT k-1 (2) where k is a constant number, R is universal gas constant, T is temperature, P. P2, and P. are pressures. In multi-stage compression, T, P., and P2 are fixed. Prove that the work is minimized if Pc = (PP)0.5. Hint: Think about how a function can be minimized. Minimize work, and then it's mostly just moving terms around