A house with a 15.1x 10 3 ft 2 floor areaand 8.50 ft high ceilings is to be heat

Question

A house with a 15.1x 103 ft2 floor areaand 8.50 ft high ceilings is to be heated with propane. How manykilograms of propane would be needed to raise the temperature ofthe air inside the house from 62.0o F to
74.0o F ?. In this calculation you are ignoring thetemperature of the walls etc.

The molar specific heat of the air inside the house is 30.2 Jmol-1oC-1
The average density of air over this temperature range can beestimated to be 1.22 g/L.
The molar mass of air is 29.1 g/mol.
There are 28.317 liters in a cubic foot.
The molar heat of combustion of propane is -2220.047 kJ/mol

Explanation / Answer

Volume of the house = area x height = 128350 ft3 =3.63 x 106 L           Mass of air enclosed = density x volume = 4.43 x106 gms              No. of moles of air enclosed = mass/molar mass = 1.52 x105 moles When temperature is converted to celcius, change intemperature = 23.33 - 16.67 = 6.67o C                   Heat required = heat density x no. of moles x change intemperature = 3.07 x 107 J                               No. of moles of propane = heat generated/heat ofcombustion of propane = 13.81 moles                Mass of propane generated = 13.81 x 44 gms = 607.93gms           Therefore, 607.93 gms of propane are required

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