A hot-air balloon roughly spherical in shape has a volume of 70,000 \(\mathrm{ft}^{3}\) and a weight of \(500 \mathrm{lb}\) (including passengers, basket, balloon fabric, etc.). If the outside air temperature is \(80^{\circ} \mathrm{F}\) and the temperature within the balloon is \(165^{\circ} \mathrm{F}\), estimate the rate at which it will rise under steady-state conditions if the atmospheric pressure is \(14.7 \mathrm{psi}\).