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A heat engine working on the Carnot cycle receives heat at the rate of 40 kW from a source at 1200 K and rejects to a sink at 300 K. The heat rejected is _______.
- a)5 kW
- b)10 kW
- c)20 kW
- d)30 kW
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A heat engine working on the Carnot cycle receives heat at the rate of...
The efficiency of a Carnot engine can be used to calculate the heat rejected (Qc) using the formula:
η = 1 - (Tcold / Thot)
Where:
η is the efficiency
Tcold is the absolute temperature of the cold reservoir (in Kelvin)
Thot is the absolute temperature of the hot reservoir (in Kelvin)
Given:
Thot = 1200 K
Tcold = 300 K
Efficiency (η) = 1 - (Tcold / Thot)
Calculations:
η = 1 - (300 K / 1200 K) = 0.75
Now, we can calculate the heat input (Q_hot) and then find the heat rejected (Q_c):
η = Qhot / Qhot
0.75 = 40 kW / Qhot
Solving for Qhot:
Qhot = (0.75) * (40 kW) = 30 kW
Now, to find the heat rejected (Qc), we can use the conservation of energy:
Qc = Qhot - Work done
Since it's a Carnot engine, the work done is given by the efficiency times the heat input:
Work done = η * Qhot = (0.75) * (30 kW) = 22.5 kW
Qc = 30 kW - 22.5 kW = 7.5 kW
So, the heat rejected is 7.5 kW. Therefore, the correct answer is Option B.
η = 1 - (Tcold / Thot)
Where:
η is the efficiency
Tcold is the absolute temperature of the cold reservoir (in Kelvin)
Thot is the absolute temperature of the hot reservoir (in Kelvin)
Given:
Thot = 1200 K
Tcold = 300 K
Efficiency (η) = 1 - (Tcold / Thot)
Calculations:
η = 1 - (300 K / 1200 K) = 0.75
Now, we can calculate the heat input (Q_hot) and then find the heat rejected (Q_c):
η = Qhot / Qhot
0.75 = 40 kW / Qhot
Solving for Qhot:
Qhot = (0.75) * (40 kW) = 30 kW
Now, to find the heat rejected (Qc), we can use the conservation of energy:
Qc = Qhot - Work done
Since it's a Carnot engine, the work done is given by the efficiency times the heat input:
Work done = η * Qhot = (0.75) * (30 kW) = 22.5 kW
Qc = 30 kW - 22.5 kW = 7.5 kW
So, the heat rejected is 7.5 kW. Therefore, the correct answer is Option B.
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Community Answer
A heat engine working on the Carnot cycle receives heat at the rate of...
Understanding the Carnot Cycle
The Carnot cycle is a theoretical model that defines the maximum efficiency a heat engine can achieve based on the temperatures of the heat source and sink. The efficiency (η) of a Carnot engine is given by the formula:
η = 1 - (T_sink / T_source)
Where:
- T_sink = Temperature of the cold reservoir (in Kelvin)
- T_source = Temperature of the hot reservoir (in Kelvin)
Given Data
- Heat received from source (Q_in) = 40 kW
- T_source = 1200 K
- T_sink = 300 K
Calculating Efficiency
Using the efficiency formula:
- η = 1 - (300 K / 1200 K)
- η = 1 - 0.25
- η = 0.75 (or 75%)
Calculating Work Done
The work done (W) by the engine can be calculated as:
W = η * Q_in
Substituting the values:
- W = 0.75 * 40 kW
- W = 30 kW
Calculating Heat Rejected
The heat rejected (Q_out) to the sink can be found using the first law of thermodynamics:
Q_out = Q_in - W
Substituting the values:
- Q_out = 40 kW - 30 kW
- Q_out = 10 kW
Conclusion
Thus, the heat rejected to the sink is:
10 kW
Therefore, the correct answer is option B.
The Carnot cycle is a theoretical model that defines the maximum efficiency a heat engine can achieve based on the temperatures of the heat source and sink. The efficiency (η) of a Carnot engine is given by the formula:
η = 1 - (T_sink / T_source)
Where:
- T_sink = Temperature of the cold reservoir (in Kelvin)
- T_source = Temperature of the hot reservoir (in Kelvin)
Given Data
- Heat received from source (Q_in) = 40 kW
- T_source = 1200 K
- T_sink = 300 K
Calculating Efficiency
Using the efficiency formula:
- η = 1 - (300 K / 1200 K)
- η = 1 - 0.25
- η = 0.75 (or 75%)
Calculating Work Done
The work done (W) by the engine can be calculated as:
W = η * Q_in
Substituting the values:
- W = 0.75 * 40 kW
- W = 30 kW
Calculating Heat Rejected
The heat rejected (Q_out) to the sink can be found using the first law of thermodynamics:
Q_out = Q_in - W
Substituting the values:
- Q_out = 40 kW - 30 kW
- Q_out = 10 kW
Conclusion
Thus, the heat rejected to the sink is:
10 kW
Therefore, the correct answer is option B.
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A heat engine working on the Carnot cycle receives heat at the rate of 40 kW from a source at 1200 K and rejects to a sink at 300 K. The heat rejected is _______.a)5 kWb)10 kWc)20 kWd)30 kWCorrect answer is option 'B'. Can you explain this answer?
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