Concept explainers
(a)
To Calculate: The number of moles of Helium gas contained in the balloon.
(a)
Explanation of Solution
Given:
Load,
weight of the balloon’s envelope,
Volume of the balloon when it is fully inflated,
Temperature of air,
Atmospheric pressure,
Net upward force on balloon,
Formula Used:
Ideal gas law:
Here, P is the pressure, V is the volume, R is the gas constant, n is the number of moles and T is the temperature.
Buoyant force can be obtained by:
here,
Calculations:
Density of air,
Density of helium,
Substitute the values and solve:
Conclusion:
Thus, the number of moles of Helium gas contained in the balloon is
(b)
To Find:The altitudeat which the balloon would be fully inflated.
(b)
Explanation of Solution
Given:
Load,
weight of the balloon’s envelope,
Volume of the balloon when it is fully inflated,
Temperature of air,
Atmospheric pressure,
Net upward force on balloon,
Formula Used:
Variation of pressure with altitude ( h ):
From ideal gas law:
Here, P is the pressure, V is the volume, R is the gas constant, n is the number of moles and T is the temperature.
Calculations:
Substitute the values and solve:
Conclusion:
Thus, the altitude at which the balloon would be fully inflated is 4.7 km.
(c)
Whether the balloon would ever reach the altitude at which it is fully inflated.
(c)
Explanation of Solution
Given:
Load,
Weight of the balloon’s envelope,
Volume of the balloon when it is fully inflated,
Temperature of air,
Atmospheric pressure,
Net upward force on balloon,
Formula Used:
In order to reach the altitude at which the balloon is fully inflated, the buoyant force
Calculations:
Substitute the values and solve:
Because
Conclusion:
Yes, the balloon would ever reach the altitude at which it is fully inflated.
(d)
The maximum altitude attained by the balloon.
(d)
Explanation of Solution
Given:
Load,
Weight of the balloon’s envelope,
Volume of the balloon when it is fully inflated,
Temperature of air,
Atmospheric pressure,
Net upward force on balloon,
Formula Used:
The balloon will rise till the net force on it is zero.
Calculations:
Substitute the values and solve:
Conclusion:
The maximum altitude attained by the balloon is
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Chapter 17 Solutions
Physics for Scientists and Engineers
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