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Hot air balloons are open at their lower and end. A basket is suspended from the balloon and can take several passengers as well as the pilot. A propane burner fixed to the basket is used to heat up the air in the balloon A hot balloon has a volume of 1500 m3 and its volume does not change when the enclosed air is heated.

1) Use the ideal gas equation, pV=nRT. to calculate how many molecules of the balloon contains at a temperature of 10 °C and a pressure 10.1 KP.
2) Calculate the mass of air it contains, assuming an average M of 29.​

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onyebuchinnaji

(a) The number of molecules contained by the balloon at the given condition is 6,438.97 moles.

(b) The mass of air in the balloon is 186.73 kg.

The given parameters;

  • volume of the balloon, V = 1500 m³
  • temperature, T = 10⁰C = 273 + 10 = 283 K
  • pressure, = P = 10.1 kPa = 10,100 Pa

The number of molecules contained by the balloon at the given condition is calculated as follows;

[tex]PV = nRT[/tex]

where;

  • R is ideal gas constant = 8.314 J/mol.K
  • n is the number of moles air in the balloon;

[tex]n = \frac{PV}{RT} \\\\n = \frac{10,100 \times 1500}{8.314 \times 283} \\\\n = 6,438.97 \ moles[/tex]

The mass of air in the balloon is calculated as;

[tex]n = \frac{m}{M} \\\\m = nM\\\\m = 6,438.97\ moles \ \times \ 29 \ g/mol\\\\m = 186.73 \ kg[/tex]

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