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Consider a Carnot heat engine which receives heat at 750 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -15°C at a rate of 400 kJ/min and rejects it to the same environment at 300 K.
The rate of heat supplied ( in kJ/min) to the heat engine will be (Answer up to one decimal place)
    Correct answer is '108.5'. Can you explain this answer?
    Most Upvoted Answer
    Consider a Carnot heat engine which receives heat at 750 K and rejects...
    °C. Find the coefficient of performance of the refrigerator.

    To find the coefficient of performance (COP) of the refrigerator, we need to determine the ratio of the heat removed from the cooled space to the work input to the refrigerator.

    First, let's convert the temperatures to Kelvin:
    T1 (hot reservoir temperature) = 750 K
    T2 (cold reservoir temperature) = 300 K
    T3 (cooled space temperature) = -15°C + 273.15 = 258.15 K

    The efficiency of the Carnot heat engine is given by the formula:
    η = 1 - (T2 / T1)

    η = 1 - (300 K / 750 K)
    η = 1 - 0.4
    η = 0.6

    Since the entire work output of the heat engine is used to drive the refrigerator, the work input to the refrigerator is equal to the work output of the heat engine.

    The work input to the refrigerator is given by the formula:
    W_in = Q_in - Q_out

    Since the work output of the heat engine is equal to Q_in, we have:
    W_in = Q_in - Q_out = Q_out

    The heat removed from the cooled space is given by the formula:
    Q_out = m * C * ΔT

    Where:
    m = mass of the substance being cooled
    C = specific heat capacity of the substance being cooled
    ΔT = change in temperature of the substance being cooled

    Assuming the mass of the substance being cooled is 1 kg and the specific heat capacity is constant, we can calculate the heat removed from the cooled space:
    Q_out = 1 kg * C * (T3 - T2)

    Now, we can calculate the work input to the refrigerator:
    W_in = Q_out = 1 kg * C * (T3 - T2)

    Finally, we can calculate the COP of the refrigerator using the formula:
    COP = Q_out / W_in = 1 / (T3 - T2)

    COP = 1 / (258.15 K - 300 K)
    COP = 1 / (-41.85 K)

    Therefore, the coefficient of performance of the refrigerator is approximately -0.024.
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    Community Answer
    Consider a Carnot heat engine which receives heat at 750 K and rejects...
    A Carnot heat engine drives a Carnot refrigerator that removes heat from a cold medium at a specified rate.
    The coefficient of performance of the Carnot refrigerator is
    Then, the power input to the refrigerator becomes
    which is equal to the power output of the heat engine . The thermal efficiency of the Carnot heat engine is
    Then, from the definition of thermal efficiency, the rate of heat input to this heat engine is
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    Consider a Carnot heat engine which receives heat at 750 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -15°C at a rate of 400 kJ/min and rejects it to the same environment at 300 K.The rate of heat supplied ( in kJ/min) to the heat engine will be (Answer up to one decimal place)Correct answer is '108.5'. Can you explain this answer?
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    Consider a Carnot heat engine which receives heat at 750 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -15°C at a rate of 400 kJ/min and rejects it to the same environment at 300 K.The rate of heat supplied ( in kJ/min) to the heat engine will be (Answer up to one decimal place)Correct answer is '108.5'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider a Carnot heat engine which receives heat at 750 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -15°C at a rate of 400 kJ/min and rejects it to the same environment at 300 K.The rate of heat supplied ( in kJ/min) to the heat engine will be (Answer up to one decimal place)Correct answer is '108.5'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a Carnot heat engine which receives heat at 750 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -15°C at a rate of 400 kJ/min and rejects it to the same environment at 300 K.The rate of heat supplied ( in kJ/min) to the heat engine will be (Answer up to one decimal place)Correct answer is '108.5'. Can you explain this answer?.
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