Question

Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. Is the work positive, negative or zero?

Answer 1

The boundary work is: W = ⌡P dV

P drops but does V go up or down?

The process equation is: PVn = C

so we can solve for P to show it in a P-V diagram

P = CV-n

as n = 1.667 the curve drops as V goes up we see

V2 > V1 giving dV > 0 and the work is then positive.