The efficiency of a carnot cycle is 1/6. If on reducing the temperature of the sink 75 degree Celsius, the efficiency becomes 1/3, determine

Question

The efficiency of a carnot cycle is 1/6. If on reducing the temperature of the sink 75 degree Celsius, the efficiency becomes 1/3, determine the initial and final temperature between which the cycle is working.

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Thành Công 5 months 2021-08-15T15:23:47+00:00 1 Answers 7 views 0

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    2021-08-15T15:25:45+00:00

    Answer:

    375 and 450

    Explanation:

    The computation of the initial and the final temperature is shown below:

    In condition 1:

    The efficiency of a Carnot cycle is \frac{1}{6}

    So, the equation is

    \frac{1}{6} = 1 - \frac{T_2}{T_1}

    For condition 2:

    Now if the temperature is reduced by 75 degrees So, the efficiency is \frac{1}{3}

    Therefore the next equation is

    \frac{1}{3} = 1 - \frac{T_2 - 75}{T_1}

    Now solve both the equations

    solve equations (1) and (2)

    2(1 - T_2/T_1) = 1 - (T_2 - 75)/T_1\\\\2 - 1 = 2T_2/T_1 - (T_2 - 75)/T_1\\\\ = (T_2 + 75)/T_1T_1 = T_2 + 75\\\Now\ we\ will\ Put\ the\ values\ into\ equation (1)\\\\1/6 = 1 - T_2/(T_2 + 75)\\\\1/6 = (75)/(T_2 + 75)

    T_2 + 450 = 75

    T_2 = 375

    Now put the T_2 value in any of the above equation

    i.e

    T_1 = T_2 + 75

    T_1 = 375 + 75

    = 450

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