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5.37 At steady state, a power cycle develops a power output of 10 kW while receiving energy by heat transfer at the rate of 10 kJ per cycle of operation from a source at temperature T. The cycle rejects energy by heat transfer to cooling water at a lower temperature of 300 K. If there are 100 cycles per minute, what is the minimum theoretical value for T, in K?

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  1. Today, 10:58
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    Answer: minimum theoretical value of T = 750k

    Explanation:

    Assuming the the cycle is reversible and is ideal then

    Wnet/Qh = Nmin ... equa 1

    Equation 1 can be rewritten as

    (Th - TL) / Th ... equation 2

    Th = temp of hot reservoir

    TL = temp of low reservoir = 300

    Wnet = power generated=10kw

    He = energy transfer=10kj per cycle

    Qhe = power transfer = (100/60) * 10Kj = 16.67kw

    Sub into equat 1

    Nmin = 10/16.67 = 0.6

    Sub Nmin into equation 2

    Th = - TL / (Nmin - 1) = - 300k / (0.6 - 1)

    Th = 750k
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