Answer :
Final answer:
The temperature of the air inside the balloon must reach a certain value in order for it to succeed in lifting 187 kg. This temperature can be calculated using the principles of buoyancy and the ideal gas law.
Explanation:
To determine the temperature required for the hot air balloon to lift a mass of 187 kg, we can use the principles of buoyancy and the ideal gas law.
First, let's calculate the buoyant force required to lift the balloon and the mass. The buoyant force is equal to the weight of the air displaced by the balloon, which is given by the equation:
Buoyant force = density of air * volume of balloon * acceleration due to gravity
Since the balloon is filled with hot air, its density is lower than the density of the surrounding air. The density of air can be calculated using the ideal gas law equation:
Density of air = (mass of air * molar mass of air) / (volume of air * gas constant * temperature)
Substituting the given values, we have:
Density of air = (mass of air * molar mass of air) / (volume of air * gas constant * temperature)
Now, let's solve for the temperature:
Temperature = (mass of air * molar mass of air) / (density of air * volume of air * gas constant)
Substituting the given values, we have:
Temperature = (187 kg * 29 g/mol) / (density of air * 1037 m * gas constant)
By solving this equation, we can find the temperature required for the hot air balloon to lift a mass of 187 kg.
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