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11 September, 09:15

An air conditioner takes outside air at 35°C and cools it to 15°C at a rate of 1 kg/s. Estimate the amount of power needed to do this. Recalculate the needed power if it is put in recirculation mode using inside air at 24°C and cools that to 15°C.

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  1. 11 September, 09:21
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    Q=20.1kW

    recirculation mode=Q=9.045kW

    Explanation:

    Hi!

    To solve this problem you must use the first law of thermodynamics that establishes the energy that enters a system is the same that must come out. Given the above we have the following equation

    Q = mCp (T2-T1)

    WHERE

    Q = Heat removed to air

    m = mass air flow = 1kg / s

    Cp = specific heat of air = 1.005KJ / kg °C

    T2 = air inlet temperature

    T1 = air outlet temperature=15°C.

    for the first case

    Q = (1kg/s) (1.005KJ/kg°C) (35°C-15°C)

    Q=20.1kW

    for the second case (recirculation mode)

    Q = (1kg/s) (1.005KJ/kg°C) (24°C-15°C)

    Q=9.045kW
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