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The more effective way of increasing the efficiency of a Carnot engine is to
- a)increase higher temperature
- b)decrease higher temperature
- c)increase lower temperature
- d)decrease lower temperature
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The more effective way of increasing the efficiency of a Carnot engine...
(decreasing lower temperature by ΔT)
(increasing higher temperature by ΔT)
So, the more effective way to increase the cycle efficiency is to decrease lower temperature.
Most Upvoted Answer
The more effective way of increasing the efficiency of a Carnot engine...
Increasing the efficiency of a Carnot engine by decreasing the lower temperature
To understand why decreasing the lower temperature of a Carnot engine is the more effective way to increase its efficiency, we need to have a basic understanding of how a Carnot engine works.
What is a Carnot engine?
A Carnot engine is an idealized engine that operates on the reversible Carnot cycle. It consists of two isothermal processes and two adiabatic processes. The engine operates between two heat reservoirs, a higher temperature reservoir (TH) and a lower temperature reservoir (TL).
The Carnot efficiency
The efficiency of a Carnot engine is given by the Carnot efficiency formula:
Efficiency = 1 - (TL / TH)
Where TL is the lower temperature and TH is the higher temperature.
Effect of decreasing the lower temperature on efficiency
When we decrease the lower temperature (TL) while keeping the higher temperature (TH) constant, the efficiency of the Carnot engine increases. This is because the Carnot efficiency formula shows that the efficiency is inversely proportional to the ratio of TL to TH.
Explanation
1. The Carnot efficiency formula reveals that as TL decreases, the ratio TL/TH decreases, resulting in an increase in efficiency.
2. This can be understood by considering the heat transfer during the isothermal expansion and isothermal compression processes of the Carnot cycle.
3. During the isothermal expansion process, heat is transferred from the higher temperature reservoir to the working fluid, and during the isothermal compression process, heat is transferred from the working fluid to the lower temperature reservoir.
4. By decreasing TL, the temperature difference between the working fluid and the lower temperature reservoir decreases, resulting in less heat being transferred during the isothermal compression process.
5. As less heat is transferred during the isothermal compression process, less heat is wasted, and therefore, the efficiency of the engine increases.
Conclusion
Decreasing the lower temperature (TL) of a Carnot engine is the more effective way to increase its efficiency. This is because it reduces the temperature difference between the working fluid and the lower temperature reservoir, resulting in less wasted heat during the isothermal compression process.
To understand why decreasing the lower temperature of a Carnot engine is the more effective way to increase its efficiency, we need to have a basic understanding of how a Carnot engine works.
What is a Carnot engine?
A Carnot engine is an idealized engine that operates on the reversible Carnot cycle. It consists of two isothermal processes and two adiabatic processes. The engine operates between two heat reservoirs, a higher temperature reservoir (TH) and a lower temperature reservoir (TL).
The Carnot efficiency
The efficiency of a Carnot engine is given by the Carnot efficiency formula:
Efficiency = 1 - (TL / TH)
Where TL is the lower temperature and TH is the higher temperature.
Effect of decreasing the lower temperature on efficiency
When we decrease the lower temperature (TL) while keeping the higher temperature (TH) constant, the efficiency of the Carnot engine increases. This is because the Carnot efficiency formula shows that the efficiency is inversely proportional to the ratio of TL to TH.
Explanation
1. The Carnot efficiency formula reveals that as TL decreases, the ratio TL/TH decreases, resulting in an increase in efficiency.
2. This can be understood by considering the heat transfer during the isothermal expansion and isothermal compression processes of the Carnot cycle.
3. During the isothermal expansion process, heat is transferred from the higher temperature reservoir to the working fluid, and during the isothermal compression process, heat is transferred from the working fluid to the lower temperature reservoir.
4. By decreasing TL, the temperature difference between the working fluid and the lower temperature reservoir decreases, resulting in less heat being transferred during the isothermal compression process.
5. As less heat is transferred during the isothermal compression process, less heat is wasted, and therefore, the efficiency of the engine increases.
Conclusion
Decreasing the lower temperature (TL) of a Carnot engine is the more effective way to increase its efficiency. This is because it reduces the temperature difference between the working fluid and the lower temperature reservoir, resulting in less wasted heat during the isothermal compression process.
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The more effective way of increasing the efficiency of a Carnot engine...
B
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