The work done by the gas is: (d) 287.68
The work done by the gas in an isobaric process (constant pressure) when the pressure is inversely proportional to the volume can be calculated using the formula:
W = P × ΔV × ln(Vf/Vi)
where:
W is the work done,
P is the pressure,
ΔV is the change in volume, and
ln is the natural logarithm.
Given an initial volume (Vi) of 3 cubic feet, a final volume (Vf) of 4 cubic feet, and an initial pressure of 1000 pounds per square foot, we can substitute these values into the formula to find the work done.
W = 1000 × (4−3) × ln(4/3)
W = 1000 × 1 × 0.28768
W = 1000 × 0.28768
W = 287.68
Therefore, the work done by the gas is 287.68 pounds per square foot. Hence, the correct answer is (d) 287.68.