Chapter 15, Problem 71PQ

The density of air in the Earth’s atmosphere decreases according to the function $\rho ={\rho }_0{e}^{-h/h_0}$, where ${\rho }_0=1.20{\text{ kg/m}}^3$ is the density of air at sea level and h₀ is the scale height of the atmosphere, with an average value of 7640 m. What is the maximum payload that a balloon filled with 2.50 × 10³ m³ of helium ( ${\rho }_{\text{He}}=0.179{\text{ kg/m}}^3$) can lift to an altitude of 10.0 km?