Arrange the following isothermal processes in order of the magnitude of the work (p − V) involved between states 1 and 2. Choose the correct option.
- |wB| > |wA| > |wC| > |wD|
- |wC| > |wD| > |wA| > |wB|
- |wC| > |wD| > |wB| > |wA|
- |wB| > |wA| > |wD| > |wC|
Answer
(3) |wC| > |wD| > |wB| > |wA|
Solution
For an isothermal change between the same two states, |w| = area under the p–V path.
Expansion (work done by the gas, against pext lower than the gas pressure):
Single stage — whole expansion against the final (lowest) pressure ⇒ smallest area ⇒ |wA| is the least
Multi stage — higher external pressure in the early steps ⇒ larger area ⇒ |wB| > |wA|
Compression (work done on the gas, by pext higher than the gas pressure):
Single stage — whole compression at the final (highest) pressure ⇒ largest area ⇒ |wC| is the greatest
Multi stage — lower external pressure in the early steps ⇒ smaller area ⇒ |wC| > |wD|
∵ every compression path lies above the reversible isotherm and every expansion path lies below it
⇒ |wD| > |wrev| > |wB|
∴ |wC| > |wD| > |wB| > |wA|
Answer: (3)