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26 December, 18:42

A Carnot engine whose high-temperature reservoir is at 620 k takes in 550 J of heat at this temperature in each cycle and gives up 335 J to the low temperature reservoir.

(a) How much mechanical work does the engine perform during each cycle?

(b) What is the temperature of the low-pressure reservoir?

(c) What is the thermal efficiency of the cycle?

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  1. 26 December, 19:23
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    (a) W=217 J

    (b) Tc=378K

    (c) e=0.39=39%

    Explanation:

    For part (a)

    We to calculate the mechanical work W the engine does. By knowing QC and QH can obtain the work using equation

    W = IQHI - IQcl ... eq (1)

    Put given values for QH and QC into equation (1) to get

    the mechanical work of the engine

    W = 550 - 335

    W=217 J

    For part (b)

    We want to determine the temperature of low temperature reservoir which means Tc

    IQc|/|Qh| = TC/TH

    for Tc

    Tc = (IQc|/|Qh|) * TH

    Now we can put values

    Tc = 620K (335 / 550.1)

    Tc=378K

    For part (c)

    Here we want to find the thermal efficiency (e) of the cycle

    e=1-TC/TH

    e=1 - (378/620)

    e=0.39=39%
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