Hot-Air Balloon
The mass of a hot-air balloon and its cargo (not including the air inside) is 200kg. The air outside is at 10.0°C and 101kPa. The volume of the balloon is 400m
3
. To what temperature must the air in the balloon be heated before the balloon will lift off? (Air density at 10.0°C is 1.25kg/m
3
.)
Mass of Balloon = 200 kg
At T
1
= 10.0°C = 283K
Density of air, ρ
c
= 1.25 kg/m
3
At high temp, T
2
=
_
K
Density of air, ρ
h
=
ρ
c
T
1
/
T
2
(ρ
c
-ρ
h
)gV = mg
T =
10
°C
Density of hot air is lower than the cold air surrounding the Hor-air Balloon
THEORY / CALCULATION
F = mg
B = (ρ
c
- ρ
h
)gV