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A heat pump operating on the Carnot cycle pumps heat from a reservoir at 300 K to a reservoir at 600 K. The coefficient of performance is
- a)1.5
- b)0.5
- c)2
- d)1
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A heat pump operating on the Carnot cycle pumps heat from a reservoir ...
Given data
T2 = 300 K
T1 = 600 K
(COP)HP = T1 / T1 - T2
= 600 / 600 - 300
= 2
Most Upvoted Answer
A heat pump operating on the Carnot cycle pumps heat from a reservoir ...
Explanation:
A heat pump is a device that uses mechanical work to transfer heat from a low-temperature reservoir to a high-temperature reservoir. The coefficient of performance (COP) is a measure of the efficiency of a heat pump. It is defined as the ratio of the heat transferred to the high-temperature reservoir to the work input.
The Carnot cycle is a theoretical thermodynamic cycle that represents the most efficient operation of a heat engine or heat pump. It consists of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.
In the case of a heat pump operating on the Carnot cycle, the heat is transferred from the low-temperature reservoir at 300 K to the high-temperature reservoir at 600 K.
Process 1: Isothermal Expansion
- The heat pump absorbs heat Q1 from the low-temperature reservoir at 300 K.
- The temperature remains constant at 300 K during this process.
Process 2: Adiabatic Expansion
- The heat pump does work W on the system.
- The temperature decreases as the gas expands.
Process 3: Isothermal Compression
- The heat pump rejects heat Q2 to the high-temperature reservoir at 600 K.
- The temperature remains constant at 600 K during this process.
Process 4: Adiabatic Compression
- The heat pump does work W on the surroundings.
- The temperature increases as the gas is compressed.
The coefficient of performance (COP) for a heat pump operating on the Carnot cycle is given by the equation:
COP = Q2 / W
Since the Carnot cycle represents the most efficient operation of a heat pump, the COP is given by the Carnot efficiency equation:
COP = Th / (Th - Tl)
Where Th is the temperature of the high-temperature reservoir and Tl is the temperature of the low-temperature reservoir. In this case, Th = 600 K and Tl = 300 K.
Substituting the values into the equation, we get:
COP = 600 / (600 - 300) = 600 / 300 = 2
Therefore, the coefficient of performance (COP) for the heat pump operating on the Carnot cycle is 2. Hence, the correct answer is option 'C'.
A heat pump is a device that uses mechanical work to transfer heat from a low-temperature reservoir to a high-temperature reservoir. The coefficient of performance (COP) is a measure of the efficiency of a heat pump. It is defined as the ratio of the heat transferred to the high-temperature reservoir to the work input.
The Carnot cycle is a theoretical thermodynamic cycle that represents the most efficient operation of a heat engine or heat pump. It consists of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.
In the case of a heat pump operating on the Carnot cycle, the heat is transferred from the low-temperature reservoir at 300 K to the high-temperature reservoir at 600 K.
Process 1: Isothermal Expansion
- The heat pump absorbs heat Q1 from the low-temperature reservoir at 300 K.
- The temperature remains constant at 300 K during this process.
Process 2: Adiabatic Expansion
- The heat pump does work W on the system.
- The temperature decreases as the gas expands.
Process 3: Isothermal Compression
- The heat pump rejects heat Q2 to the high-temperature reservoir at 600 K.
- The temperature remains constant at 600 K during this process.
Process 4: Adiabatic Compression
- The heat pump does work W on the surroundings.
- The temperature increases as the gas is compressed.
The coefficient of performance (COP) for a heat pump operating on the Carnot cycle is given by the equation:
COP = Q2 / W
Since the Carnot cycle represents the most efficient operation of a heat pump, the COP is given by the Carnot efficiency equation:
COP = Th / (Th - Tl)
Where Th is the temperature of the high-temperature reservoir and Tl is the temperature of the low-temperature reservoir. In this case, Th = 600 K and Tl = 300 K.
Substituting the values into the equation, we get:
COP = 600 / (600 - 300) = 600 / 300 = 2
Therefore, the coefficient of performance (COP) for the heat pump operating on the Carnot cycle is 2. Hence, the correct answer is option 'C'.
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A heat pump operating on the Carnot cycle pumps heat from a reservoir at 300 K to a reservoir at 600 K. The coefficient of performance isa)1.5b)0.5c)2d)1Correct answer is option 'C'. Can you explain this answer?
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