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Calculate the payload when a balloon of radius 10 meter mass 1

Question

Hard

Solving time: 4 mins

Calculate the payload when a balloon of radius 10 meter mass $100 kg$ is filled with helium at $1.66$ bar at $2 7^{\circ} C$ . (Density of air $1.2 kgm^{- 3}$ and $R = 0.083$ bar $d m^{3} k^{- 1} mol^{- 1})$ .

3200 kg

3811 kg

2812 kg

2976 kg

Views: 5,328 students

Exam:

JEE Mains 2000

Found 3 tutors discussing this question

Eleanor Discussed

Calculate the payload when a balloon of radius 10 meter mass

100 kg

is filled with helium at

1.66

bar at

2 7^{\circ} C

. (Density of air

1.2 kgm^{- 3}

and

R = 0.083

bar

d m^{3} k^{- 1} mol^{- 1})

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Volume of balloon

= \frac{4}{3} π r^{3} = \frac{4}{3} (\frac{22}{7}) (10)^{3} = 4190.47 m^{3}

= 4190.47 \times 1 0^{3} L

Mass of dry air

= d \times v = 1.2 \times 4190.47 = 5028.56 kg

Mass of the helium

= W = \frac{P V}{RT} \times 4 \times 1 0^{- 3} kg

= \frac{1.66 \times 4190.47 \times 1 0 ^{3} \times 4 \times 1 0 ^{- 3}}{0.083 \times 300} = 1117.45 kg

Mass of balloon with helium

= 1117.45 + 100 = 1217.45 kg

Pay load = mass of air displaced - mass of filled balloon

= 5028.56 - 1217.45 = 3811 kg

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Question Text	Calculate the payload when a balloon of radius 10 meter mass $100 kg$ is filled with helium at $1.66$ bar at $2 7^{\circ} C$ . (Density of air $1.2 kgm^{- 3}$ and $R = 0.083$ bar $d m^{3} k^{- 1} mol^{- 1})$ .
Topic	States of Matter
Subject	Chemistry
Class	Class 11
Answer Type	Text solution:1
Upvotes	92

Calculate the payload when a balloon of radius 10 meter mass $100 kg$ is filled with helium at $1.66$ bar at $2 7^{\circ} C$ . (Density of air $1.2 kgm^{- 3}$ and $R = 0.083$ bar $d m^{3} k^{- 1} mol^{- 1})$ .

Text solutionVerified

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Text solutionVerified

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Calculate the payload when a balloon of radius 10 meter mass $100 kg$ is filled with helium at $1.66$ bar at $2 7^{\circ} C$ . (Density of air $1.2 kgm^{- 3}$ and $R = 0.083$ bar $d m^{3} k^{- 1} mol^{- 1})$ .