A

To calculate the net work done by the air, we first need to calculate the torque and relate it to work.

**Step 1:** Calculate the work done by the paddle wheel.
Work (W) is calculated as:
$$ W = \tau \times \theta $$
where:
\( \tau \) = torque in ft-lbf, \( \theta \) = angular displacement in radians.

**Step 2:** We need to determine \( \theta \). The paddle wheel rotates at 100 RPM for 20 seconds.
The number of revolutions in 20 seconds is:
\( 100 \text{ rev/min} \times \frac{1 ext{ min}}{60 ext{ s}} \times 20 ext{ s} = \frac{100}{60} \times 20 \text{ rev} = \frac{2000}{60} \approx 33.33 ext{ rev} \)

Each revolution corresponds to an angular displacement of 2\(\pi\) radians:
\( \theta = 33.33 \text{ rev} \times 2\pi \text{ rad/rev} \approx 209.4 ext{ rad} \)

**Step 3:** Now, substitute \( \tau \) and \( \theta \) into the work equation:
\( W = 20 ext{ ft-lbf} \times 209.4 ext{ rad} \approx 4188 ext{ ft-lbf} \)

**Step 4:** Work done on the piston can also be calculated using the force of 500 lbf and the distance 2 ft:
\( W_{piston} = 500 ext{ lbf} \times 2 ext{ ft} = 1000 ext{ ft-lbf} \)

**Step 5:** Therefore, the net work done by the air will be the difference:
\( W_{net} = W - W_{piston} = 4188 ext{ ft-lbf} - 1000 ext{ ft-lbf} = 3188 ext{ ft-lbf} \).
Therefore, the net work done by the air is approximately 3188 ft-lbf.
Therefore, A.