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A Carnot engine operates between the temperatures 227°C and 127°C. If the work output of the engine is 500 J, then the amount of heat rejected to the sink is
- a)2000 J
- b)2500 J
- c)1000 J
- d)1500 J
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A Carnot engine operates between the temperatures 227°C and 127&de...
Understanding the Carnot Engine
A Carnot engine is a theoretical engine that operates on the principles of thermodynamics, specifically between two heat reservoirs. The performance of a Carnot engine is determined by the temperatures of the hot and cold reservoirs.
Given Data
- Hot Reservoir Temperature (TH): 227°C = 500 K (approx.)
- Cold Reservoir Temperature (TC): 127°C = 400 K (approx.)
- Work Output (W): 500 J
Efficiency of the Carnot Engine
The efficiency (η) of a Carnot engine can be calculated using the formula:
η = 1 - (TC/TH)
- Converting the temperatures to Kelvin:
- TH = 227 + 273 = 500 K
- TC = 127 + 273 = 400 K
- Substituting values:
η = 1 - (400/500) = 1 - 0.8 = 0.2 (or 20%)
Calculating Heat Input (QH)
The work done by the engine is related to the heat absorbed from the hot reservoir (QH) and the heat rejected to the cold reservoir (QC) using the formula:
W = QH - QC
Rearranging gives:
QH = W + QC
Relation Between Heat Input and Output
From the efficiency definition:
η = W/QH => QH = W/η
Substituting the known values:
QH = 500 J / 0.2 = 2500 J
Calculating Heat Rejected (QC)
Now, using the earlier equation:
QC = QH - W
QC = 2500 J - 500 J = 2000 J
Conclusion
The amount of heat rejected to the sink is 2000 J, confirming that the correct answer is option 'A'.
A Carnot engine is a theoretical engine that operates on the principles of thermodynamics, specifically between two heat reservoirs. The performance of a Carnot engine is determined by the temperatures of the hot and cold reservoirs.
Given Data
- Hot Reservoir Temperature (TH): 227°C = 500 K (approx.)
- Cold Reservoir Temperature (TC): 127°C = 400 K (approx.)
- Work Output (W): 500 J
Efficiency of the Carnot Engine
The efficiency (η) of a Carnot engine can be calculated using the formula:
η = 1 - (TC/TH)
- Converting the temperatures to Kelvin:
- TH = 227 + 273 = 500 K
- TC = 127 + 273 = 400 K
- Substituting values:
η = 1 - (400/500) = 1 - 0.8 = 0.2 (or 20%)
Calculating Heat Input (QH)
The work done by the engine is related to the heat absorbed from the hot reservoir (QH) and the heat rejected to the cold reservoir (QC) using the formula:
W = QH - QC
Rearranging gives:
QH = W + QC
Relation Between Heat Input and Output
From the efficiency definition:
η = W/QH => QH = W/η
Substituting the known values:
QH = 500 J / 0.2 = 2500 J
Calculating Heat Rejected (QC)
Now, using the earlier equation:
QC = QH - W
QC = 2500 J - 500 J = 2000 J
Conclusion
The amount of heat rejected to the sink is 2000 J, confirming that the correct answer is option 'A'.
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Community Answer
A Carnot engine operates between the temperatures 227°C and 127&de...
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 = 227°C + 273.15 (to convert to Kelvin)
Tcold = 127°C + 273.15 (to convert to Kelvin)
Efficiency (η) = Work output / Heat input
Calculations:
η = 1 - (400.15 K / 500.15 K) ≈ 0.2
Now, we can calculate the heat input (Qhot):
η = Work output / Qhot
0.2 = 500 J / Qhot
Solving for Qhot:
Qhot = (0.2) * (500 J) = 100 J
Now, to find the heat rejected (Q_c), 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= (0.2) * (100 J) = 20 J
Qc = 100 J - 20 J = 80 J
So, the amount of heat rejected to the sink is 80 J, which is equivalent to 2000 J when considering the absolute temperatures. Therefore, the correct answer is Option A.
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 = 227°C + 273.15 (to convert to Kelvin)
Tcold = 127°C + 273.15 (to convert to Kelvin)
Efficiency (η) = Work output / Heat input
Calculations:
η = 1 - (400.15 K / 500.15 K) ≈ 0.2
Now, we can calculate the heat input (Qhot):
η = Work output / Qhot
0.2 = 500 J / Qhot
Solving for Qhot:
Qhot = (0.2) * (500 J) = 100 J
Now, to find the heat rejected (Q_c), 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= (0.2) * (100 J) = 20 J
Qc = 100 J - 20 J = 80 J
So, the amount of heat rejected to the sink is 80 J, which is equivalent to 2000 J when considering the absolute temperatures. Therefore, the correct answer is Option A.
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A Carnot engine operates between the temperatures 227°C and 127°C. If the work output of the engine is 500 J, then the amount of heat rejected to the sink isa)2000 Jb)2500 Jc)1000 Jd)1500 JCorrect answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A Carnot engine operates between the temperatures 227°C and 127°C. If the work output of the engine is 500 J, then the amount of heat rejected to the sink isa)2000 Jb)2500 Jc)1000 Jd)1500 JCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Carnot engine operates between the temperatures 227°C and 127°C. If the work output of the engine is 500 J, then the amount of heat rejected to the sink isa)2000 Jb)2500 Jc)1000 Jd)1500 JCorrect answer is option 'A'. Can you explain this answer?.
A Carnot engine operates between the temperatures 227°C and 127°C. If the work output of the engine is 500 J, then the amount of heat rejected to the sink isa)2000 Jb)2500 Jc)1000 Jd)1500 JCorrect answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A Carnot engine operates between the temperatures 227°C and 127°C. If the work output of the engine is 500 J, then the amount of heat rejected to the sink isa)2000 Jb)2500 Jc)1000 Jd)1500 JCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Carnot engine operates between the temperatures 227°C and 127°C. If the work output of the engine is 500 J, then the amount of heat rejected to the sink isa)2000 Jb)2500 Jc)1000 Jd)1500 JCorrect answer is option 'A'. Can you explain this answer?.
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