Answer:
a) Specific volume of the air in balloon is [tex]14.96 ft^3/lbm[/tex]
b)The weight of the air within the balloon is 1,126.09 lbf.
Step-by-step explanation:
Mass of air, m = 35 lbm
Volume of the air = V
Diameter of balloon = d = 10 ft
radius of the balloon = r= 0.5 d = 5 ft
Volume of balloon = V
[tex]V=\frac{4}{3}\pr r^3[/tex]
[tex]V=\frac{4}{3}\times 3.14\times (5 ft)^3[/tex]
Specific volume of the air in balloon = S
[tex]S=\frac{V}{m}=\frac{\frac{4}{3}\times 3.14\times (5 ft)^3}{35 lbm}[/tex]
[tex]S=14.96 ft^3/lbm[/tex]
Specific volume of the air in balloon is [tex]14.96 ft^3/lbm[/tex]
[tex]lbf=32.174 lbm ft/s^2[/tex]
Weight of the air = W
Acceleration due to gravity = [tex]32.174 lbm ft/s^2[/tex]
Weight = m\times g[/tex]
[tex]W=35 lbm\times 32.174 lbm ft/s^2[/tex]
[tex]W=1,126.09 lbf[/tex]
The weight of the air within the balloon is 1,126.09 lbf.
