
Concept explainers
The average temperature of the air in the balloon for the atmospheric temperature of

Answer to Problem 131RP
The average temperature of the air in the balloon for the atmospheric temperature of
The average temperature of the air in the balloon for the atmospheric temperature of
Explanation of Solution
Write the expression to obtain the buoyancy force acting on the hot-air balloon
Here, density of the cool air is
Write the expression to obtain the volume of the hot-air balloon
Here, radius of the hot-air balloon is
Write the expression to obtain the density of the cool air
Here, atmospheric pressure is P, and atmospheric air temperature is T.
Write the expression to obtain the vertical force balance acting on the hot-air balloon.
Here, weight of the hot air is
Write the expression to obtain the average temperature of the air in the balloon
Conclusion:
Consider that the air behaves as an ideal gas.
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”, obtain the gas constant of air
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the average temperature of the air in the balloon for the atmospheric temperature of
Similarly the average temperature of the air in the balloon for the atmospheric temperature of
Thus, the average temperature of the air in the balloon for the atmospheric temperature of
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