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A heat pump works on a reversed Carnot cycle. The temperature in the condenser coils is 27°C and that in the evaporator coils is –23°C. For a work input of 1 kW, how much is the heat pumped?
  • a)
    1 kW  
  • b)
    5 kW  
  • c)
    6 kW      
  • d)
    None of the above    
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A heat pump works on a reversed Carnot cycle. The temperature in the c...
For heat pump (COP) = Q1/W = T1/(T1 - T2) = 300/(300 - 250)
OR, Q1 = 6 X W = 6 X 1 = 6kW
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A heat pump works on a reversed Carnot cycle. The temperature in the c...
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A heat pump works on a reversed Carnot cycle. The temperature in the c...
Introduction:
A heat pump is a device that transfers heat from a low-temperature reservoir to a high-temperature reservoir. It operates on a reversed Carnot cycle, which is an ideal cycle that consists of four processes: isothermal compression, adiabatic compression, isothermal expansion, and adiabatic expansion. In this case, the temperature in the condenser coils is 27°C and in the evaporator coils is 23°C.

Explanation:
To determine the heat pumped by the heat pump for a work input of 1 kW, we can use the basic equations of the Carnot cycle.

Step 1: Calculate the temperature of the hot reservoir (Th):
In this case, the temperature in the condenser coils is given as 27°C. We convert it to Kelvin by adding 273 to get:
Th = 27 + 273 = 300 K

Step 2: Calculate the temperature of the cold reservoir (Tc):
In this case, the temperature in the evaporator coils is given as 23°C. We convert it to Kelvin by adding 273 to get:
Tc = 23 + 273 = 296 K

Step 3: Calculate the coefficient of performance (COP) of the heat pump:
The COP of a heat pump is given by the ratio of the heat pumped (Qh) to the work input (W):
COP = Qh / W

Step 4: Calculate the heat pumped (Qh):
We can use the equation for the COP to find the heat pumped:
COP = Qh / W
1 = Qh / 1
Qh = 1 kW

Conclusion:
The heat pumped by the heat pump for a work input of 1 kW is 1 kW. Therefore, option 'a' is the correct answer.
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