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A closed auditorium of volume 27100 m^3 is filled with 2210 people at the beginning of a show, and the air in the space is at a temperature of 292 K and a pressure of 1.013·10^5 Pa. If there were no ventilation, by how much would the temperature (in K) of the air rise during the 1.5-h show if each person metabolizes at a rate of 73.1 W?

  • physics -

    heat= massair*specifichat*deltatemp

    moles air=PV/RT then mass air= 27*molesair in grams.

    Now, use the first equatio to find deltaTemp

  • physics -

    Assume that the persons' bodies remain at the same temperature and that the heat they generate goes into the air. That is not a bad assumption.

    Q = heat generated
    = 2210*73.1 J/s * 5400 s
    = 8.72*10^8 J

    The specific heat at constant volume of the air is
    Cv = (5/2)R
    = 4.97 calories/mole K
    = 20.77 J/mole K

    Since there is no ventilation, it is assumed that the air cannot get out as the temperature rises. If the air can escape, then use
    Cp = (7/2)R

    Use n = PV/RT for the number of moles
    n = 27.1*10^3*1.013·10^5/(8.317*292) = 1.13*10^6 moles

    delta T = Q/(n*Cv) = ? degrees K or C

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