A hot air balloon has a volume of 2000 m³ when fully inflated,and the air inside the balloon is always at atmospheric pressure because of the large opening used to fill the balloon and heat the air inside it.What's the mass of hot air inside the balloon if its temperature is 120°C? (Assume a molecular weight of 28.8 g/mole for air. ) A)1790 kg B)5850 kg C)203 kg D)62.0 kg E)None of the above

Question

Quizplus · Accepted Answer

The mass of hot air inside the balloon can be calculated using the ideal gas law:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.Since the air inside the balloon is always at atmospheric pressure, we can assume that P = 1 atm. We are also given that V = 2000 m^3 and T = 120°C = 393 K. The molecular weight of air is given as 28.8 g/mole, so the molar mass of air is 28.8 g/mol.Using the ideal gas law, we can solve for the number of moles of air inside the balloon:n = PV/RT = (1 atm)(2000 m^3)/(0.0821 Latm/(molK))(393 K) = 1000 molFinally, we can calculate the mass of hot air inside the balloon by multiplying the number of moles by the molar mass:mass = n * molar mass = (1000 mol)(28.8 g/mol) = 28800 g = 28.8 kgTherefore, the mass of hot air inside the balloon is 28.8 kg, which is closest to choice A, 1790 kg.

A Hot Air Balloon Has a Volume of 2000 M3

A Hot Air Balloon Has a Volume of 2000 M³