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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 18 / Problem 63P

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Solved: CP A balloon of volume 750 m3 is to be filled with

Chapter 18, Problem 63P

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QUESTION:

Problem 63P

CP A balloon of volume 750 m3 is to be filled with hydrogen at atmospheric pressure (1.01 X 105 Pa). (a) If the hydrogen is stored in cylinders with volumes of 1.90 m3 at a gauge pressure of 1.20 X 106 Pa, how many cylinders are required? Assume that the temperature of the hydrogen remains constant. (b) What is the total weight (in addition to the weight of the gas) that can be supported by the balloon if both the gas in the balloon and the surrounding air are at 15.0o C? The molar mass of hydro-gen (H2) is 2.02 g/mol. The density of air at 15.0o C and atmospheric pressure is 1.23 kg/m3.See Chapter 12 for a discussion of buoyancy. (c) What weight could be supported if the balloon were filled with helium (molar mass 4.00 g/mol) instead of hydrogen, again at 15.0o C?

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QUESTION:

Problem 63P

CP A balloon of volume 750 m3 is to be filled with hydrogen at atmospheric pressure (1.01 X 105 Pa). (a) If the hydrogen is stored in cylinders with volumes of 1.90 m3 at a gauge pressure of 1.20 X 106 Pa, how many cylinders are required? Assume that the temperature of the hydrogen remains constant. (b) What is the total weight (in addition to the weight of the gas) that can be supported by the balloon if both the gas in the balloon and the surrounding air are at 15.0o C? The molar mass of hydro-gen (H2) is 2.02 g/mol. The density of air at 15.0o C and atmospheric pressure is 1.23 kg/m3.See Chapter 12 for a discussion of buoyancy. (c) What weight could be supported if the balloon were filled with helium (molar mass 4.00 g/mol) instead of hydrogen, again at 15.0o C?

ANSWER:

Solution 63P

Step 1:

Given data:

Density of air is ${\rho{}}_{air}=1.23kg/{m}^{3}$

Mass of hydrogen is ${M}_{H2}=2.2\times{}1{0}^{-3}\ kg/mol$

Mass of helium is ${M}_{He}=4.0\times{}1{0}^{-3}\ kg/mol$

Volume of balloon $V=750{\ m}^{3}$

Acceleration due to gravity is $g=9.8\ m/{s}^{2}\$

Atmospheric pressure of hydrogen $P=1.01\times{}1{0}^{6}\ Pa$

Universal real gas constant $R=8.314\ J/kg.mol$

Temperature of hydrogen $T=288.15\ K$

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