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10 June, 08:55

A hot air balloon is filled with 1.37 * 106 l of an ideal gas on a cool morning (11 °c. the air is heated to 117 °c. what is the volume of the air in the balloon after it is heated? assume that none of the gas escapes from the balloon.

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  1. 10 June, 11:05
    0
    So according to Charles's law the volume of a gas is directly proportional to the absorbed absolute temperature assuming constant pressure and a closed system. Or V/T=constant.

    (V1/T1) = (V2/T2). Absolute temperature is in degrees Kelvin so:

    T1=273.15+11 = 284.15 K and T2=273.15 + 117=390.15 K. V1 = 1.37*10^6 L.

    We need to find V2. V2 = (V1/T1) * T2.

    Now we plug in the numbers: V2 = (1.37*10^6/284.15) * 390.15=1881068.1 L.

    The volume of the air balloon when we heat the gas inside is

    V2=1.88*10^6 L.
  2. 10 June, 11:30
    0
    We first assume the gas is an ideal gas so we can use the equation PV = nRT. At constant pressure, nR/P are constants so at any condition the ratio of V/T is the same. With this, we calculate as follows:

    V1/T1 = k = V2/T2

    1.37 * 10^6 L / (11+273.15) = V2 / (117+273.15)

    V2 = 1881068.1 L
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