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The COP of a Carnot refrigeration cycle decreases on
- a)Decreasing the difference in operating temperatures
- b)Keeping the upper temperature constant and increasing the lower temperature
- c)Increasing the upper temperature and keeping the lower temperature constant
- d)Increasing the upper temperature and decreasing the lower temperature
Correct answer is option 'C'. Can you explain this answer?
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The Carnot Refrigeration Cycle
The Carnot refrigeration cycle is a theoretical refrigeration cycle that consists of four processes: two isothermal processes and two adiabatic processes. It is considered the most efficient refrigeration cycle possible.
Coefficient of Performance (COP) of a Refrigeration Cycle
The coefficient of performance (COP) is a measure of the efficiency of a refrigeration cycle. It is defined as the ratio of the heat extracted from the cold reservoir to the work input to the system. Mathematically, it can be expressed as:
COP = Qc / W
where COP is the coefficient of performance, Qc is the heat extracted from the cold reservoir, and W is the work input to the system.
Effect of Temperature Difference on COP
The COP of a Carnot refrigeration cycle decreases when the difference in operating temperatures decreases. This can be explained using the formula for COP:
COP = Qc / W
In a Carnot refrigeration cycle, the heat extracted from the cold reservoir (Qc) is directly proportional to the temperature difference between the hot and cold reservoirs. Therefore, as the temperature difference decreases, the heat extracted also decreases. This results in a lower COP.
Effect of Increasing Upper Temperature and Keeping Lower Temperature Constant on COP
When the upper temperature is increased and the lower temperature is kept constant, the COP of a Carnot refrigeration cycle increases. This can be explained as follows:
As the upper temperature increases, the heat extracted from the cold reservoir (Qc) also increases. This is because the temperature difference between the hot and cold reservoirs increases. Since the work input (W) remains constant, an increase in Qc results in a higher COP.
Conclusion
In the given options, the correct answer is option 'C' - increasing the upper temperature and keeping the lower temperature constant. This is because increasing the upper temperature increases the heat extracted from the cold reservoir, leading to a higher COP. The other options do not result in an increase in COP.
The Carnot refrigeration cycle is a theoretical refrigeration cycle that consists of four processes: two isothermal processes and two adiabatic processes. It is considered the most efficient refrigeration cycle possible.
Coefficient of Performance (COP) of a Refrigeration Cycle
The coefficient of performance (COP) is a measure of the efficiency of a refrigeration cycle. It is defined as the ratio of the heat extracted from the cold reservoir to the work input to the system. Mathematically, it can be expressed as:
COP = Qc / W
where COP is the coefficient of performance, Qc is the heat extracted from the cold reservoir, and W is the work input to the system.
Effect of Temperature Difference on COP
The COP of a Carnot refrigeration cycle decreases when the difference in operating temperatures decreases. This can be explained using the formula for COP:
COP = Qc / W
In a Carnot refrigeration cycle, the heat extracted from the cold reservoir (Qc) is directly proportional to the temperature difference between the hot and cold reservoirs. Therefore, as the temperature difference decreases, the heat extracted also decreases. This results in a lower COP.
Effect of Increasing Upper Temperature and Keeping Lower Temperature Constant on COP
When the upper temperature is increased and the lower temperature is kept constant, the COP of a Carnot refrigeration cycle increases. This can be explained as follows:
As the upper temperature increases, the heat extracted from the cold reservoir (Qc) also increases. This is because the temperature difference between the hot and cold reservoirs increases. Since the work input (W) remains constant, an increase in Qc results in a higher COP.
Conclusion
In the given options, the correct answer is option 'C' - increasing the upper temperature and keeping the lower temperature constant. This is because increasing the upper temperature increases the heat extracted from the cold reservoir, leading to a higher COP. The other options do not result in an increase in COP.
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The COP of a Carnot refrigeration cycle decreases ona)Decreasing the difference in operating temperatures b)Keeping the upper temperature constant and increasing the lower temperature c)Increasing the upper temperature and keeping the lower temperature constant d)Increasing the upper temperature and decreasing the lower temperatureCorrect answer is option 'C'. Can you explain this answer?
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