Answer: -1038.8 kJ
Explanation:
From the question, we can see that PV^n = constant. And as such, we can deduce that it is a polytropic process. Thus, we can use the polytropic work equation to calculate the needed work input.
from the question we were given
Mass of nitrogen, m = 7kg
initial temperature, T1 = 250k
Final temperature, T2 = 450k
Polytropic index, n = 1.4
Specific gas constant, R = 0.2968kJ/kgK
W = [p2 * v2 - p1 * v1] / 1 - n
W = [m * R * T2 - T1] / 1 - n
W = 7*0.2968*(450 - 250)] / 1 - 1.4
W = [7*0.2968*200] / -0.4
W = 415.52 / -0.4
W = -1038.8 kJ
