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प्रश्न
Payload is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the payload when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at 27°C. (Density of air = 1.2 kg m–3 and R = 0.083 bar dm3 K–1 mol–1).
उत्तर
Given,
Radius of the balloon, r = 10 m
∴ Volume of the balloon = `4/3pi"r"^3`
`= 4/3 xx22/7 xx 10^3`
`= 4190.5 " m"^3 ("approx")`
Thus, the volume of the displaced air is 4190.5 m3.
Given,
Density of air = 1.2 kg m–3
Then, mass of displaced air = 4190.5 × 1.2 kg
= 5028.6 kg
Now, mass of helium (m) inside the balloon is given by,
`"m" = ("MpV")/("RT")`
Here
`"M" = 4 xx 10^(-3) "kg mol"^(-1)`
p = 1.66 bar
V = Volume of the balloon
= `4190.5 " m"^3`
`"R" = 0.083 " bar" " dm"^3 "K"^(-1) "mol"^(-1)`
`"T" = 27^@"C" = 300 "K"`
Then `"m" = (4xx10^(-3)xx1.66xx4190.5xx10^3)/(0.083 xx300)`
= 1117.5 kg (approx)
Now, total mass of the balloon filled with helium = (100 + 1117.5) kg
= 1217.5 kg
Hence, pay load = (5028.6 – 1217.5) kg
= 3811.1 kg
Hence, the pay load of the balloon is 3811.1 kg.
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