A 2.00 mol sample of nitrogen gas is confined in a variable-volume piston
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A 2.00 mol sample of nitrogen gas is confined in a variable-volume piston. Beginning at 350 K and 5.0 atm, the gas is taken through the three-segment path described below and the work done by the external pressure is negligible.
Segment 1: Isothermal compression to 30 atm at 350 K
Segment 2: Isochoric cooling from 350 K to 250 K at 30 atm
Segment 3: Isothermal compression from 30 atm to 120 atm at 250 K
(a) For each segment, state whether the deviation of the gas from ideal behavior is expected to increase, decrease, or reverse its sign. Support each answer with molecular-level reasoning that clearly identifies the dominant effect.
(b) Construct a qualitative P–V sketch for the entire path that indicates where Z<1, Z=1, and Z>1. Label any approximate crossover points.
(c) Determine during which of the three segments the magnitude of the deviation ∣Z−1∣ is likely to be greatest. Justify fully.
(d) Propose one modification to the path (change in temperature or pressure range) that would eliminate any region where Z<1 while still reaching a final pressure near 120 atm. Explain why your modification works.