Final answer:
The P-V work done by the compressed air on the surroundings to inflate the bounce house from 201 L to 17700 L against a constant atmospheric pressure of 0.987 atm is -17283.013 L·atm.
Step-by-step explanation:
The amount of P-V work done by the compressed air to inflate a bounce house can be calculated using the formula work = -PΔV, where P is the constant external pressure and ΔV is the change in volume. Using the given values, P equals 0.987 atm, and ΔV is the final volume minus the initial volume which is 17700 L - 201 L = 17499 L. Thus, the work done is:
Work = -PΔV
Work = -(0.987 atm)(17499 L)
Work = -17283.013 L·atm
The work here is negative because it is done by the system on the surroundings, thereby reducing the system's energy. In this context, liter atmospheres (L·atm) is the unit of work.