Calculating Work Done by a Gas Expansion

[IniquiTrance]

Homework Statement

A gas is initially at (20 Pa, 3 m³) and expands to (30 Pa, 17 m³).

The minimum amount of pressure the gas can be under is 9 Pa, and the maximum pressure the gas can be under is 40 Pa.

Find the minimum amount of work that can be done by the gas in going from its initial state to its final state.

Homework Equations

W = P\DeltaV

The Attempt at a Solution

The statement doesn't state whether heat is added to the system, or whether the gas temperature changes. If the temperature varies, then P, V, and T all vary, so not sure how to approach this.

p.s., the answer provided is 126 J.

Thanks!

 

[hikaru1221]

Well, a tricky one
They only ask for the work done by the gas, so focus on it. They leave you no clue about the process, so you can make up any process, as long as the work is minimum and the pressure doesn't go beyond its limits.
My suggestion: Draw the P-V diagram, and in that diagram, draw a path from point (20 Pa, 3m^3) to point (30 Pa, 17m^3) so that the area under the path is minimum, as the work = that area. You will see that the maximum pressure has no important role in this problem, only the minimum one does