A weather ballon is prepared to lift off at the North Pole. The balloon is filled with 15000 L of helium gas. The conditions at the launch site are 760 mm Hg and 0 degrees celsius. The balloon is then released and rises to a height of 20,000 m. The atmospheric pressure decreases at a rate of 0.0032mm Hg per meter. The temperture drops at a rate of 0.001 celcius per meter. At 15,000 m the balloon reaches its maximum unpressurized volume of 82.5 kl, at which time the internal pressure begins to increase at a rate of 10mm Hg per 100L increase. The balloon ultimately reaches it maximum volume of 90kL at 19,500m. What is the density g/m of the helium gas at 20,000m? How many molecules of He2 are in the balloon (assuming no loss)?

Question

A weather ballon is prepared to lift off at the North Pole.  The balloon is filled with 15000 L of helium gas.  The conditions at the launch site are 760 mm Hg and 0 degrees celsius.  The balloon is then released and rises to a height of 20,000 m.  The atmospheric pressure decreases at a rate of 0.0032mm Hg per meter.  The temperture drops at a rate of 0.001 celcius per meter.  At 15,000 m the balloon reaches its maximum unpressurized volume of 82.5 kl, at which time the internal pressure begins to increase at a rate of 10mm Hg per 100L increase.  The balloon ultimately reaches it maximum volume of 90kL at 19,500m. What is the density g/m of the helium gas at 20,000m? How many molecules of He2 are in the balloon (assuming no loss)?