CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $$ 10 m , $$ mass $$100 kg $$ is filled with helium at $$ 1.66 $$ bar at $$27^o C ( $$ Density of air $$ = 1.2 kg m^{-3} $$ and $$ R = 0.83 $$ bar $$dm^3 K^{-1} mol^{-1} ) . $$


A
1138.12 Kg
loader
B
3811.12 Kg
loader
C
1381.12 Kg
loader
D
3112.38 kg
loader

Solution

The correct option is D $$3811.12$$ Kg
Payload of the ballon = mass of the displaced air- mass of the ballon
Radius of the ballon, $$r=10m$$
Mass of the ballon, $$m=100kg$$
Therefore volume of the ballon $$=4.3nr^3=4/3\times 22/7\times (10)^3=4190.5\, m^3$$
Now volume of the displaced air $$=4190.5\,m^3$$
Given :
Density of air $$=1.2\, kg\,m^{-3}$$
Therefore, the mass of the displaced air $$=4190.5\times 1.2=5028.6\,kg$$
Let $$w$$ be the mass of helium gas filled into the ballon, then 
$$PV=(w/m)RT$$
OR $$w=PVM/RT$$
$$=(1.66\times 4190.5\times 10^3\times 4)/(0.083\times 300)$$
$$=1117\,kg$$ (approx)
Total mass of the balloon filled with He $$=1117+100=1217\,kg$$
Therefore payload of the balloon $$=5028.6-1217=3811.6\,kg$$
Hence,m the pay load of the balloon is $$3811.6\,kg$$
Therefore, the correct option is B.

Chemistry

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image