It is known that density `rho` of air decreases with height y as
`rho=rho_0e^(-y//y_0)`
where `rho_0=1.25 kg m^-3` is the density at sea level. And `y_0` is a constant . This density variation is called the law of atmosphere. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value of g remains constant.
A large He balloon of volume `1425 m^3` is used to lift a payload of 400kg.Assume that the balloon maintains constant radius as it rises. How high does it rise?

Explanation

8km, If we consider the variation of g with altitude the height is somewhat more. About 8.2km.