The total mass that can be lifted by a balloon is given by the difference between the mass of air displaced by the balloon and the mass of the gas inside the balloon. Consider a hot-air balloon that approximates a sphere. 5.00 m in diameter and contains air heated to 65^oC. The surrounding air temperature is 21^oC. The pressure in the balloon is equal to the atmospheric pressure, which is 745 torr.

a. What total mass can the balloon lift? Assume the average molar mass of air is 29.0 g/ mol. (Hint: Heated air is less dense than cool air.)

b. If the balloon is filled with enough helium at 21^oC and 745 torr to achieve the same volume as in part a, what total mass can the balloon lift?

c. What mass could the hot- air balloon (from part a) lift if it were on the ground in Denver, Colorado, where a typical atmospheric pressure is 630. torr?

d. What mass could the hot- air balloon (from part a) lift if it were a cold day with a temperature of 28^oC?