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A Carnot heat engine is working with an efficiency of 50%. If the cycle is converted into a heat pump after reversing, then what is the coefficient of performance of the heat pump?
- a)1
- b)1.67
- c)2
- d)2.5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A Carnot heat engine is working with an efficiency of 50%. If the cyc...
The efficiency of Carnot engine (ηE) = 50%
ηE=1−TLTH=0.5
Now, this is converted to the heat pump,
Dividing by TH
Short trick:
If a Carnot heat engine which is operating between two temperature limits is converted to a heat pump, then
Most Upvoted Answer
A Carnot heat engine is working with an efficiency of 50%. If the cyc...
Efficiency of a Carnot heat engine is given by the formula:
Efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
Given that the efficiency of the Carnot heat engine is 50% or 0.5, we can rewrite the formula as:
0.5 = 1 - (Tc/Th)
Rearranging the equation, we have:
Tc/Th = 1 - 0.5
Tc/Th = 0.5
This equation represents the ratio of the temperatures of the cold and hot reservoirs.
When the Carnot cycle is reversed and converted into a heat pump, the roles of the hot and cold reservoirs are interchanged. The cold reservoir of the heat engine becomes the hot reservoir of the heat pump, and vice versa. Therefore, the new temperature ratio for the heat pump can be written as:
Th/Tc = 1 / (Tc/Th)
Th/Tc = 1 / 0.5
Th/Tc = 2
The coefficient of performance (COP) of a heat pump is given by the formula:
COP = Th / (Th - Tc)
Substituting the value of Th/Tc from the previous equation, we have:
COP = 2 / (2 - 1)
COP = 2 / 1
COP = 2
Therefore, the coefficient of performance of the heat pump is 2, which corresponds to option C.
Efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
Given that the efficiency of the Carnot heat engine is 50% or 0.5, we can rewrite the formula as:
0.5 = 1 - (Tc/Th)
Rearranging the equation, we have:
Tc/Th = 1 - 0.5
Tc/Th = 0.5
This equation represents the ratio of the temperatures of the cold and hot reservoirs.
When the Carnot cycle is reversed and converted into a heat pump, the roles of the hot and cold reservoirs are interchanged. The cold reservoir of the heat engine becomes the hot reservoir of the heat pump, and vice versa. Therefore, the new temperature ratio for the heat pump can be written as:
Th/Tc = 1 / (Tc/Th)
Th/Tc = 1 / 0.5
Th/Tc = 2
The coefficient of performance (COP) of a heat pump is given by the formula:
COP = Th / (Th - Tc)
Substituting the value of Th/Tc from the previous equation, we have:
COP = 2 / (2 - 1)
COP = 2 / 1
COP = 2
Therefore, the coefficient of performance of the heat pump is 2, which corresponds to option C.
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A Carnot heat engine is working with an efficiency of 50%. If the cycle is converted into a heat pump after reversing, then what is the coefficient of performance of the heat pump?a)1b)1.67c)2d)2.5Correct answer is option 'C'. Can you explain this answer?
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