When does gas do more work: constant pressure or temperature?

[Sudikshya Pant]

A quantity of ideal gas undergoes an expansion that doubles its volume. Does the gas do more work on its surroundings if the expansion is at constant pressure or at constant temperature?

The answer in the book says W at constant temperature gives a greater value for the given case.

But when I tried to solve it mathematically, I got greater value of W at constant pressure which is plain wrong. I don't understand where did I go wrong.

For constant pressure my result was:

W = p(2V-V) =pV = (nRT/V)*V =nRT

For constant temperature my result was:
W= nRT ln(2V/V) =nRT ln(2) =0.69 nRT

So, I got lesser value for constant temperature than constant pressure.

Where did I went wrong?

 

[Chestermiller]

If both cases start out at the same pressure and volume (and temperature), then the constant pressure does more work.

 

[kuruman]

I don't think you went wrong anywhere. If you draw a pV diagram of the two processes, starting at the same point, the area under each curve is the work done by the gas. At constant pressure, you have a line parallel to the volume axis while the isotherm drops below it.