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Three engines A, B and C operating on Carnot cycle respectively use air, steam and Helium as the working fluid. If all the engine operates within the same temperature limit, then which engine will have highest efficiency.
- a)Engine A
- b)Engine B
- c)Engine C
- d)All engines will have same efficiency
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Three engines A, B and C operating on Carnot cycle respectively use ai...
Since efficiency of the engine purely depends upon source and sink temperatures and independent of the working substances. All the engines have same efficiency.
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Three engines A, B and C operating on Carnot cycle respectively use ai...
The Carnot Cycle
The Carnot cycle is a theoretical thermodynamic cycle that represents the most efficient possible heat engine operating between two constant temperature reservoirs. It consists of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The efficiency of a Carnot cycle is given by the formula:
Efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
Comparison of Engine Efficiency
In this scenario, three engines A, B, and C are operating on the Carnot cycle. Engine A uses air as the working fluid, engine B uses steam, and engine C uses helium. The question states that all three engines operate within the same temperature limit.
Since all the engines operate within the same temperature limit, the hot reservoir temperature (Th) is the same for all the engines. Therefore, the efficiency of the engines can be determined by comparing the temperature of the cold reservoir (Tc) for each engine.
Temperature Limit
Let's assume that the temperature limit for all the engines is T. In this case, the efficiency of each engine can be calculated as follows:
- Engine A: Efficiency_A = 1 - (Tc_A/T)
- Engine B: Efficiency_B = 1 - (Tc_B/T)
- Engine C: Efficiency_C = 1 - (Tc_C/T)
Same Efficiency
Since all the engines operate within the same temperature limit, the efficiency of each engine is determined by the ratio of the cold reservoir temperature to the temperature limit. As a result, all three engines will have the same efficiency. Therefore, the correct answer is option 'D', i.e., all engines will have the same efficiency.
Conclusion
In summary, when engines operate on the Carnot cycle within the same temperature limit, the efficiency of the engines solely depends on the ratio of the cold reservoir temperature to the temperature limit. As a result, all engines will have the same efficiency.
The Carnot cycle is a theoretical thermodynamic cycle that represents the most efficient possible heat engine operating between two constant temperature reservoirs. It consists of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The efficiency of a Carnot cycle is given by the formula:
Efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
Comparison of Engine Efficiency
In this scenario, three engines A, B, and C are operating on the Carnot cycle. Engine A uses air as the working fluid, engine B uses steam, and engine C uses helium. The question states that all three engines operate within the same temperature limit.
Since all the engines operate within the same temperature limit, the hot reservoir temperature (Th) is the same for all the engines. Therefore, the efficiency of the engines can be determined by comparing the temperature of the cold reservoir (Tc) for each engine.
Temperature Limit
Let's assume that the temperature limit for all the engines is T. In this case, the efficiency of each engine can be calculated as follows:
- Engine A: Efficiency_A = 1 - (Tc_A/T)
- Engine B: Efficiency_B = 1 - (Tc_B/T)
- Engine C: Efficiency_C = 1 - (Tc_C/T)
Same Efficiency
Since all the engines operate within the same temperature limit, the efficiency of each engine is determined by the ratio of the cold reservoir temperature to the temperature limit. As a result, all three engines will have the same efficiency. Therefore, the correct answer is option 'D', i.e., all engines will have the same efficiency.
Conclusion
In summary, when engines operate on the Carnot cycle within the same temperature limit, the efficiency of the engines solely depends on the ratio of the cold reservoir temperature to the temperature limit. As a result, all engines will have the same efficiency.
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Three engines A, B and C operating on Carnot cycle respectively use air, steam and Helium as the working fluid. If all the engine operates within the same temperature limit, then which engine will have highest efficiency.a)Engine Ab)Engine Bc)Engine Cd)All engines will have same efficiencyCorrect answer is option 'D'. Can you explain this answer?
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