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Answer :
Final answer:
The work done during the inflation process is approximately 1465.4 kJ.
Explanation:
To calculate the work done during the inflation process, we follow these steps:
1. Calculate the initial volume of the balloon using the formula for the volume of a sphere: V = (4/3) * π * r^3, where r is the radius (half the diameter). Given the diameter is 15.5 m, the radius is r = 15.5 / 2 = 7.75 m. Therefore, the initial volume V_initial = (4/3) * π * (7.75)^3.
2. Calculate the final volume of the balloon after inflation. Since the diameter increases by 15.5 m, the new radius is r_new = 7.75 + 15.5 / 2 = 15.5 m. The final volume V_final = (4/3) * π * (15.5)^3.
3. Calculate the change in volume ΔV = V_final - V_initial.
4. Use the ideal gas law to calculate the work done: W = P * ΔV, where P is the pressure and ΔV is the change in volume.
5. Substitute the given pressure of 97.7 kPa and the calculated ΔV into the formula to find the work done in joules.
6. Convert the work done from joules to kilojoules by dividing by 1000.
Calculating these values step by step, we find the work done during the inflation process is approximately 1465.4 kJ.
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