How to calculate Payload of a Balloon?

Payload of a Balloon if defined as maximum mass which a Balloon can carry with in it upward direction.

If V is the volume of Balloon , d_out is the density of out side air , d_in is the density of gas inside of Balloon  and Maas of Balloon is m then

Payload= [d_out × V]- [d-in×V+m]

Related Questions;

(1) Calculate payload of a balloon having volume 100 litre. It is filled with helium gas at 0.2486 atm pressureand 300K. Density of air is 1.3 gm/litre and mass of material of balloon is 20 gm.

(2) A balloon of diameter 20 m weighs 100 kg. Calculate its paylod if it is filled with helium at 1.0 atm and 27 ∘ C. Density of air is 1.2 kg m −3 .(R=0.082 dm 3 atm K −1 mol −1 ).

Air Bubbles in water, or lake temperature, lake depth, related Questions.

(1) The diameters of a buble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm and the temperature of the lake-water and the atmosphere are equal what is the depth of the lake ? (The density of lake-water and Hg are 1 gm/ml and 13.6 respectively. Also neglect the contribution of pressure due to surface tension)

(2) Radius of bubble X-1 is 0.32 cm and X-2 is 0.48 cm. What is the temperature of of pond at the position of bubble X-2. If presure of the Bottom of the pond is 2.8 atm and at the top is 1 atm.

(3) A bubble of gas released at bottom. of the lake increase to four time its original volume when it reach the surface. assuming that atmosphere ic pressure is equivalent to the exerted by a column of water 10 m height. What is the depth of the lake.

(4) An air bubble starts rising from the bottom of lake, it diameter is 3.6 mm at bottom and 4 mm at the surface. The depth of lake is 250 cm and temperature at surface is 40℃ . What is the temperature at the bottom of lake? (Given atmospheric pressure = 76 cm of Hg and g= 980 cm sec-1 neglect surface tension effect).