A ballon with volume 4200m^3 is filled with helium gas at 27°C,1 bar pressure and found to be weight 700 kg.The density of air is 1.2 kg m^-3 the payload of ballon is
Answers
Answer:
Explanation:
The volume of the balloon is V=
3
4
πr
3
.
The radius of balloon is 10 m.
Hence, the volume of the balloon is V=
3
4
×3.1416×(10)
3
=4186.7m
3
.
The mass of displaced air is obtained from the product of volume and density. It is 4186.7×1.2=5024.04kg.
The number of moles of gas present are n=
RT
PV
=
0.083×300
1.666×4186.7×10
3
=279.11×10
3
.
Note: Here, the unit of volume is changed from m
3
to dm
3
.
1m
3
=1000dm
3
.
Mass of helium present is obtained by multiplying the number of moles with molar mass. It is 279.11×10
3
×4=1116.44×10
3
g=1116.4 kg.
The mass of filled balloon is the sum of the mass of the empty ballon and the mass of He. It is 100+1116.4=1216.4 kg.
Pay load = mass of displaced air − mass of balloon =5024.04−1216.44=3807.6 kg