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A heat engine receives heat from a source at 1500 K at a rate of 600 kW and rejects the waste heat to a medium at 350 K. If the power output from the heat engine is 250 kW, the irreversibility rate for the process is
- a)125 kW
- b)150 kW
- c)180 kW
- d)210 kW
Correct answer is option 'D'. Can you explain this answer?
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Understanding the Heat Engine Operation
A heat engine operates by converting heat energy into mechanical work. In this scenario, we have the following parameters:
- Heat input (Q_in) = 600 kW
- Power output (W_out) = 250 kW
- Heat rejected (Q_out) = ?
Calculating Heat Rejected
To find the heat rejected, we can use the first law of thermodynamics:
Q_in = W_out + Q_out
Rearranging gives us:
Q_out = Q_in - W_out
Substituting the values:
Q_out = 600 kW - 250 kW = 350 kW
Evaluating the Efficiency
The efficiency (η) of the heat engine can be calculated as:
η = W_out / Q_in
Thus,
η = 250 kW / 600 kW = 0.4167 or 41.67%
Calculating the Theoretical Efficiency
For a Carnot engine, the maximum theoretical efficiency can be determined using the temperatures of the heat source (T_hot) and the heat sink (T_cold):
η_carnot = 1 - (T_cold / T_hot)
Substituting the temperatures:
η_carnot = 1 - (350 K / 1500 K) = 1 - 0.2333 = 0.7667 or 76.67%
Determining the Irreversibility Rate
Irreversibility (I) can be calculated as the difference between the work output of an ideal engine and the actual work output.
Ideal work output (W_ideal) = η_carnot * Q_in
W_ideal = 0.7667 * 600 kW = 460 kW
Now, the irreversibility rate:
I = W_ideal - W_out = 460 kW - 250 kW = 210 kW
Conclusion
Thus, the irreversibility rate for the heat engine process is 210 kW, corresponding to option 'D'.
A heat engine operates by converting heat energy into mechanical work. In this scenario, we have the following parameters:
- Heat input (Q_in) = 600 kW
- Power output (W_out) = 250 kW
- Heat rejected (Q_out) = ?
Calculating Heat Rejected
To find the heat rejected, we can use the first law of thermodynamics:
Q_in = W_out + Q_out
Rearranging gives us:
Q_out = Q_in - W_out
Substituting the values:
Q_out = 600 kW - 250 kW = 350 kW
Evaluating the Efficiency
The efficiency (η) of the heat engine can be calculated as:
η = W_out / Q_in
Thus,
η = 250 kW / 600 kW = 0.4167 or 41.67%
Calculating the Theoretical Efficiency
For a Carnot engine, the maximum theoretical efficiency can be determined using the temperatures of the heat source (T_hot) and the heat sink (T_cold):
η_carnot = 1 - (T_cold / T_hot)
Substituting the temperatures:
η_carnot = 1 - (350 K / 1500 K) = 1 - 0.2333 = 0.7667 or 76.67%
Determining the Irreversibility Rate
Irreversibility (I) can be calculated as the difference between the work output of an ideal engine and the actual work output.
Ideal work output (W_ideal) = η_carnot * Q_in
W_ideal = 0.7667 * 600 kW = 460 kW
Now, the irreversibility rate:
I = W_ideal - W_out = 460 kW - 250 kW = 210 kW
Conclusion
Thus, the irreversibility rate for the heat engine process is 210 kW, corresponding to option 'D'.
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A heat engine receives heat from a source at 1500 K at a rate of 600 kW and rejects the waste heat to a medium at 350 K. If the power output from the heat engine is 250 kW, the irreversibility rate for the process isa)125 kWb)150 kWc)180 kWd)210 kWCorrect answer is option 'D'. Can you explain this answer?
Question Description
A heat engine receives heat from a source at 1500 K at a rate of 600 kW and rejects the waste heat to a medium at 350 K. If the power output from the heat engine is 250 kW, the irreversibility rate for the process isa)125 kWb)150 kWc)180 kWd)210 kWCorrect answer is option 'D'. 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 A heat engine receives heat from a source at 1500 K at a rate of 600 kW and rejects the waste heat to a medium at 350 K. If the power output from the heat engine is 250 kW, the irreversibility rate for the process isa)125 kWb)150 kWc)180 kWd)210 kWCorrect answer is option 'D'. 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 A heat engine receives heat from a source at 1500 K at a rate of 600 kW and rejects the waste heat to a medium at 350 K. If the power output from the heat engine is 250 kW, the irreversibility rate for the process isa)125 kWb)150 kWc)180 kWd)210 kWCorrect answer is option 'D'. Can you explain this answer?.
A heat engine receives heat from a source at 1500 K at a rate of 600 kW and rejects the waste heat to a medium at 350 K. If the power output from the heat engine is 250 kW, the irreversibility rate for the process isa)125 kWb)150 kWc)180 kWd)210 kWCorrect answer is option 'D'. 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 A heat engine receives heat from a source at 1500 K at a rate of 600 kW and rejects the waste heat to a medium at 350 K. If the power output from the heat engine is 250 kW, the irreversibility rate for the process isa)125 kWb)150 kWc)180 kWd)210 kWCorrect answer is option 'D'. 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 A heat engine receives heat from a source at 1500 K at a rate of 600 kW and rejects the waste heat to a medium at 350 K. If the power output from the heat engine is 250 kW, the irreversibility rate for the process isa)125 kWb)150 kWc)180 kWd)210 kWCorrect answer is option 'D'. Can you explain this answer?.
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