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17 December, 02:07

An air-conditioning system operating on the reversed Carnot cycle is required to transfer heat from a house at a rate of 755 kJ/min to maintain its temperature at 24°C. If the outdoor air temperature is 35°C, determine the power required to operate this air-conditioning system.

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  1. 17 December, 02:25
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    There is 0.466 KW required to operate this air-conditioning system

    Explanation:

    Step 1: Data given

    Heat transfer rate of the house = Ql = 755 kJ/min

    House temperature = Th = 24°C = 24 + 273 = 297 Kelvin

    Outdoor temperature = To = 35 °C = 35 + 273 = 308 Kelvin

    Step 2: Calculate the coefficient of performance o reversed carnot air-conditioner working between the specified temperature limits.

    COPr, c = 1 / ((To/Th) - 1)

    COPr, c = 1 / ((308/297) - 1)

    COPr, c = 1 / 0.037

    COPr, c = 27

    Step 3: The power input cna be given as followed:

    Wnet, in = Ql / COPr, max

    Wnet, in = 755 / 27

    Wnet, in = 27.963 kJ/min

    Win = 27.963 * 1 KW/60kJ/min = 0.466 KW

    There is 0.466 KW required to operate this air-conditioning system
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