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?

It is known that density rho of air decreases with height y as rho=rh

1.	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?
Answer» Solution :8KM, If we CONSIDER the variation of g with ALTITUDE the height is somewhat more. About 8.2km.