A 1kg non-stretch balloon fabric can form a spherical balloon with a maximum radius of 5m. It is attached to a 2kg payload.The fabric is slowly inflated on the ground (?0 = 1 bar) with helium until the balloon just lifts off. Just lifts off means that the balloon is close to buoyancy equilibrium. It remains close to equilibrium as the balloon continues to rise and expand. The balloon stops rising when it reaches its full size. Assume an isothermal atmosphere at -10 degrees C and ideal gas behavior. Non-stretch fabric means the pressure inside the balloon equals the outside pressure at all times. Assume the temperature of the helium equals the outside air temperature. Take air to be (20 mol % oxygen, 80 mol % nitrogen).
a. What mass of helium was placed in balloon?
b. What altitude does the balloon reach?
Use barometric formula and buoyancy formula.