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A refrigerator operates between the temperatures of –23ºC and 27ºC. If one TR = 3.5 kW, the minimum power required per TR to operate the refrigerator is
- a)0.5 kW
- b)0.7 kW
- c)0.9 kW
- d)1.0 kW
Correct answer is option 'B'. Can you explain this answer?
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A refrigerator operates between the temperatures of –23ºC a...
= 0.7 kW
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A refrigerator operates between the temperatures of –23ºC a...
To determine the minimum power required per TR to operate the refrigerator, we need to use the Carnot cycle efficiency formula. The Carnot cycle is a theoretical thermodynamic cycle that describes the most efficient heat engine possible operating between two temperatures.
1. Identify the temperatures:
The refrigerator operates between two temperatures: 23°C (T1) and 27°C (T2).
2. Convert temperatures to Kelvin:
To use the Carnot cycle efficiency formula, we need to convert the temperatures to Kelvin. The Kelvin temperature scale starts at absolute zero, which is -273.15°C.
T1 = 23 + 273.15 = 296.15 K
T2 = 27 + 273.15 = 300.15 K
3. Calculate the Carnot cycle efficiency:
The Carnot cycle efficiency (η) is given by the formula:
η = (T1 - T2) / T1
Substituting the values:
η = (296.15 - 300.15) / 296.15
η = -4 / 296.15
η ≈ -0.0135
4. Calculate the minimum power required per TR:
The minimum power required per TR can be calculated using the formula:
Power per TR = Power / TR
Given that one TR is equal to 3.5 kW, we can calculate the minimum power per TR:
Power per TR = 3.5 kW / TR
5. Determine the correct option:
To find the minimum power required per TR, we need to consider the absolute value of the efficiency since power cannot be negative. The correct option will be the one that corresponds to the smallest power per TR.
Substituting the efficiency value:
Power per TR = 3.5 kW / TR ≈ 0.0135
Comparing this value with the provided options, we can see that option B, 0.7 kW, is the closest value.
Therefore, the correct answer is option B, 0.7 kW.
1. Identify the temperatures:
The refrigerator operates between two temperatures: 23°C (T1) and 27°C (T2).
2. Convert temperatures to Kelvin:
To use the Carnot cycle efficiency formula, we need to convert the temperatures to Kelvin. The Kelvin temperature scale starts at absolute zero, which is -273.15°C.
T1 = 23 + 273.15 = 296.15 K
T2 = 27 + 273.15 = 300.15 K
3. Calculate the Carnot cycle efficiency:
The Carnot cycle efficiency (η) is given by the formula:
η = (T1 - T2) / T1
Substituting the values:
η = (296.15 - 300.15) / 296.15
η = -4 / 296.15
η ≈ -0.0135
4. Calculate the minimum power required per TR:
The minimum power required per TR can be calculated using the formula:
Power per TR = Power / TR
Given that one TR is equal to 3.5 kW, we can calculate the minimum power per TR:
Power per TR = 3.5 kW / TR
5. Determine the correct option:
To find the minimum power required per TR, we need to consider the absolute value of the efficiency since power cannot be negative. The correct option will be the one that corresponds to the smallest power per TR.
Substituting the efficiency value:
Power per TR = 3.5 kW / TR ≈ 0.0135
Comparing this value with the provided options, we can see that option B, 0.7 kW, is the closest value.
Therefore, the correct answer is option B, 0.7 kW.
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A refrigerator operates between the temperatures of –23ºC and 27ºC. If one TR = 3.5 kW, the minimum power required per TR to operate the refrigerator isa)0.5 kW b)0.7 kW c)0.9 kW d)1.0 kWCorrect answer is option 'B'. Can you explain this answer?
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