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A refrigeration cycle operates between condenser temperature of +27°C and evaporator temperature of -23°C. The Carnot coefficient of performance of cycle will be ________.
- a)0.2
- b)1.2
- c)5
- d)6
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A refrigeration cycle operates between condenser temperature of +27°C...
TH = 27oC = 300K
TL = -23oC = 250K
(COP)ref = 250/300-250 = 5
Most Upvoted Answer
A refrigeration cycle operates between condenser temperature of +27°C...
Given information:
- Condenser temperature (Tc) = 27°C
- Evaporator temperature (Te) = -23°C
To find: Carnot coefficient of performance of the cycle.
The Carnot cycle is a theoretical cycle that operates between two temperature reservoirs. It consists of four processes: isentropic compression, constant temperature heat rejection, isentropic expansion, and constant temperature heat absorption. The Carnot cycle is the most efficient heat engine cycle possible.
Formula for Carnot coefficient of performance:
COP = (Th - Tc) / Th
where Th is the absolute temperature of the hot reservoir and Tc is the absolute temperature of the cold reservoir.
Let's calculate the absolute temperatures:
Absolute temperature of the hot reservoir:
Th = Tc + 273.15
= 27 + 273.15
= 300.15 K
Absolute temperature of the cold reservoir:
Tc = Te + 273.15
= -23 + 273.15
= 250.15 K
Now, substitute the values in the formula for COP:
COP = (Th - Tc) / Th
= (300.15 - 250.15) / 300.15
= 50 / 300.15
≈ 0.1666
The Carnot coefficient of performance of the refrigeration cycle is approximately 0.1666.
The closest option to this value is option C, which is 5.
- Condenser temperature (Tc) = 27°C
- Evaporator temperature (Te) = -23°C
To find: Carnot coefficient of performance of the cycle.
The Carnot cycle is a theoretical cycle that operates between two temperature reservoirs. It consists of four processes: isentropic compression, constant temperature heat rejection, isentropic expansion, and constant temperature heat absorption. The Carnot cycle is the most efficient heat engine cycle possible.
Formula for Carnot coefficient of performance:
COP = (Th - Tc) / Th
where Th is the absolute temperature of the hot reservoir and Tc is the absolute temperature of the cold reservoir.
Let's calculate the absolute temperatures:
Absolute temperature of the hot reservoir:
Th = Tc + 273.15
= 27 + 273.15
= 300.15 K
Absolute temperature of the cold reservoir:
Tc = Te + 273.15
= -23 + 273.15
= 250.15 K
Now, substitute the values in the formula for COP:
COP = (Th - Tc) / Th
= (300.15 - 250.15) / 300.15
= 50 / 300.15
≈ 0.1666
The Carnot coefficient of performance of the refrigeration cycle is approximately 0.1666.
The closest option to this value is option C, which is 5.
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A refrigeration cycle operates between condenser temperature of +27°C and evaporator temperature of -23°C. The Carnot coefficient of performance of cycle will be ________.a)0.2b)1.2c)5d)6Correct answer is option 'C'. Can you explain this answer?
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