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An ideal refrigerator has a freezer at a temperature of -130CThe coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) will be
- a)3250C
- b)325k
- c)390C
- d)3200C
Correct answer is option 'C'. Can you explain this answer?
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An ideal refrigerator has a freezer at a temperature of -130CThe coeff...
Given:
- Temperature of freezer (Tf) = -13°C = 260K
- Coefficient of performance (COP) = 5
We know that,
COP = QL / W
Where,
QL = heat extracted from the cold reservoir (freezer)
W = work done by the refrigerator
As per the question, COP = 5. Therefore,
5 = QL / W
Also, we know that,
COP = 1 + (QL / QH)
Where,
QH = heat rejected to the hot reservoir (room)
Substituting the value of COP in the above equation, we get,
5 = 1 + (QL / QH)
QL / QH = 4
Now, we can use the Carnot's theorem to find the temperature of the hot reservoir (room).
Carnot's theorem states that,
QL / QH = Tf / (Th - Tf)
Substituting the values, we get,
4 = 260 / (Th - 260)
Th - 260 = 65 * 4
Th = 520K = 247°C
Therefore, the temperature of the air (hot reservoir) to which heat is rejected is 247°C or 390K. Hence, the correct answer is option C.
- Temperature of freezer (Tf) = -13°C = 260K
- Coefficient of performance (COP) = 5
We know that,
COP = QL / W
Where,
QL = heat extracted from the cold reservoir (freezer)
W = work done by the refrigerator
As per the question, COP = 5. Therefore,
5 = QL / W
Also, we know that,
COP = 1 + (QL / QH)
Where,
QH = heat rejected to the hot reservoir (room)
Substituting the value of COP in the above equation, we get,
5 = 1 + (QL / QH)
QL / QH = 4
Now, we can use the Carnot's theorem to find the temperature of the hot reservoir (room).
Carnot's theorem states that,
QL / QH = Tf / (Th - Tf)
Substituting the values, we get,
4 = 260 / (Th - 260)
Th - 260 = 65 * 4
Th = 520K = 247°C
Therefore, the temperature of the air (hot reservoir) to which heat is rejected is 247°C or 390K. Hence, the correct answer is option C.
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An ideal refrigerator has a freezer at a temperature of -130CThe coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) will bea)3250Cb)325kc)390Cd)3200CCorrect answer is option 'C'. Can you explain this answer?
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