A helium balloon is used to lift a load of 110 N. The weight of the balloon's skin is 50 N, and the volume of the balloon when fully inflated is 32 m3. The temperature of the air is 0oC and the atmospheric pressure is 1 atm. The balloon is inflated with sufficient helium gas so that the net buoyant force on the balloon and its load is 30 N. Neglect changes of temperature with altitude.

(a) How many moles of helium gas are contained in the balloon?

(b) At what altitude will the balloon be fully inflated?

(c) Does the balloon ever reach the altitude at which it is fully inflated?

(d) If the answer to (c) is affirmative, what is the maximum altitude attained by the balloon?