Arrange the following in order of magnitude of work done by the system/on the system at constant temperature. (a) | wreversible| for expansion in infinite stages. (b) | wirreversible| for expansion in single stage. (c) | wreversible| for compression in infinite stages. (d) | wirreversible| for compression in single stage. Choose the correct answer from the options given below:
- d > c = a > b
- c = a > d > b
- a > c > b > d
- a > b > c > d
Answer
(1) d > c = a > b
Solution
Consider an ideal gas taken isothermally between the same two states (V1 and V2).
Reversible (infinite stages), either way: |w| = nRT V2V1, the area under the p–V isotherm.
a = c
Single-stage expansion against the final (lower) pressure p2: |w| = p2(V2 - V1), a rectangle lying below the isotherm.
b < a
Single-stage compression by the final (higher) pressure p1: |w| = p1(V2 - V1), a rectangle enclosing the isotherm.
d > c
d > c = a > b
(Maximum work is obtained from a reversible expansion; minimum work is needed for a reversible compression.)
Answer: (1)