A hot$-$air balloon roughly spherical in shape has a volume

of $70,000$ ft$3$

and a weight of $500$ lb $($including passengers, basket,

balloon fabric, etc.$).$ If the outside air temperature is $80$F and

the temperature within the balloon is $165$F$,$ estimate the rate at

which it will rise under steady$-$state conditions if the atmospheric

pressure is $14\mathrm{.}7$ psi.