To find:
The number of balloons that will float in air.
Answer to Problem 10.82QA
Solution:
Only one balloon filled with
Explanation of Solution
1) Concept:
We are given the density of the air, the four gases, the temperature, and the pressure. The ideal gas equation is
where
Rearranging the equation for
So, using this equation, we need to find the mass of each of the gas in the balloons. Adding the mass of empty balloons to the mass of the gas, we will get the mass of the balloon filled with a gas. Using the density formula, we calculate the density of each balloon filled with gas. Comparing the density of each balloon filled with a gas with the density of air will give number of balloons that can float in air. If the density of the balloon is equal or less than the given density of air, the balloon will float. If the density of the balloon filled with a gas is greater than the density of air, the balloon will not float. We note that among the given gases, Helium
2) Formula:
i.
ii.
iii.
3) Given:
i) Mass of empty balloon =
ii) Volume of a balloon =
iii) Four gases are:
iv) Density of air =
v) Temperature =
4) Calculations:
Using the above modified formula for mass in grams, we find mass of each gas in the balloon, and then find the mass of balloon as
i) Calculations for Helium balloon:
Mass of the balloon filled with Helium gas can be calculated as
Calculating density of each of the given gases as
Thus, density of
ii) Calculations for Neon balloon:
Mass of the balloon filled with Neon gas can be calculated as
Calculating density of each of the given gases as
Thus, density of
iii) Calculations for
Mass of the balloon filled with carbon dioxide gas can be calculated as
Calculating density of each of the given gases as
Thus, density of
iv) Calculations for
Mass of the balloon filled with carbon monoxide gas can be calculated as
Calculating density of each of the given gases as
Thus, density of
From above calculated densities of gases filled with different gases, the balloon filled with
Conclusion:
From the modified ideal gas equation, we calculated the densities of balloons filled with each gas and compared them to the given density of air. Balloons with the density equal to or less than that of air will float in air.
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Chapter 10 Solutions
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