A sample of gas expands from an initial volume of 1.0 L to a final volume of 3.0 L…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A sample of gas expands from an initial volume of 1.0 L to a final volume of 3.0 L following two different paths, A and B, that start from the same initial state (2.0 atm, 1.0 L) and end at the same final state (0.67 atm, 3.0 L).
• Path A is a straight-line change in which the pressure decreases uniformly with volume.
• Path B obeys the relation PV=k (constant).
Answer the following questions keeping the two paths in mind.
(i) Without carrying out any numerical integration or area calculation, explain which path results in a larger magnitude of work done by the gas and give a clear reason for your choice.
(ii) Describe qualitatively how the shape of a P–V curve influences the amount of work done when the initial and final volumes are fixed.