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31 August, 12:14

At steady state, a cycle develops a power output of 10 kW for heat addition at a rate of 10 kJ per cycle of operation from a source at 1500 K. Energy is rejected by heat transfer to cooling water at 300 K. Determine the minimum theoretical number of cycles required per minute.

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  1. 31 August, 12:36
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    Number of cycle per minute = 75

    Explanation:

    given data

    Power output Wnet = 10 KW

    Temperature of hot reservoir = 1500 K

    Temperature of cold reservoir = 300 K

    solution

    we know that Efficiency is express as

    n = 1 - To : Tk ... 1

    here Tk is Temperature of hot reservoir and To is Temperature of cold reservoir

    so put here value in equation 1 we get

    n = 1 - 300 : 1500

    n = 0.8

    and Rate of heat input will be

    Rate of heat input Qin = 10 * No. of cycles per sec

    Rate of heat input Qin = 10 n

    and

    n = Wnet : 10 n ... 2

    put here value

    0.8 = 10 : 10 n

    solve it we get

    n = 1.25

    so here Number of cycle per second is = 1.25

    and Number of cycle per minute will be = 1.25 * 60

    Number of cycle per minute = 75
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