Heating a room by burning butane gas. How many liters of butane must be burned to heat the room?

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You decide to heat a 10.0 ft. by 14.0 ft. by 8.00 ft room by burning butane gas, C4H10, to raise its temperature from 65.0*F to 70.0*F. The butane is stored at 10.00 atm and 65.0*F. How many liters of butane must be burned to heat the room? Assume that the air absorbed all the heat and that the room is perfectly insulated. The density and specific heat of air can be assumed to be 1.004 g/L and 1.01 J/g*C

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  • 10.0 ft. x 14.0 ft. x 8.00 ft = 1120 ft^3 = 31715 L

    70.0°F – 65.0°F = 5.0°F = 9.0°C change

    (31715 L) x (1.004 g/L) x (1.01 J/g*C) x (9.0°C) = 289443 J required

    Now you need the heat of combustion of butane.
    The source below says 2877.5 kJ/mol.

    (289.443 kJ) / (2877.5 kJ/mol) = 0.10059 mol butane

    65.0°F = 18.3°C

    PV = nRT
    V = nRT / P = (0.10059 mol) x (0.08205746 L atm/K mol) x (18.3 + 273.15 K) /
    (10.00 atm) = 0.241 L butane under the specified conditions

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