Minimum Work Input/Power Required to Freeze 50kg Water & Heat a House

AI Thread Summary
To freeze 50kg of water at 0ºC into ice, a minimum work input of 1.22x10^6J is required, accounting for both sensible and latent heat. For heating a house at 22ºC with an outside temperature of -10ºC and a heat loss of 15kW, the minimum power needed for the heat pump is 1.63kW. The discussion also touches on calculating the Carnot efficiency of the heat pump using the formula 1 - (Tc/Th). Participants express confusion over the methods to arrive at these answers, seeking clarification and procedural guidance. Overall, the thread emphasizes the importance of understanding energy transfer principles in thermodynamics.
bennyngreal
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50kg of water at 0ºC have to be frozen into ice in a refrigerator. The room temp. is 20ºC. What is the minimum work input to the refrigerator to achieve this?
(latent heat of fusion of water=3.33x10^5J/kg)
ans:1.22x10^6J

It is proposed to heat a house using a heat pump operating between the house and the outside. The hose is to be kept at 22ºC, the outside is at -10ºC and the heat loss from the house is 15kW. What is the minimum power required to operate the pump?
ans:1.63kW

Please help me to show the methods. I don't understand!
 
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bennyngreal said:
50kg of water at 0ºC have to be frozen into ice in a refrigerator. The room temp. is 20ºC. What is the minimum work input to the refrigerator to achieve this?
(latent heat of fusion of water=3.33x10^5J/kg)
ans:1.22x10^6J

The energy needed goes into decreasing the temperature of the water to 0°C (sensible heat) AND into changing the phase of the water (latent heating)

bennyngreal said:
It is proposed to heat a house using a heat pump operating between the house and the outside. The hose is to be kept at 22ºC, the outside is at -10ºC and the heat loss from the house is 15kW. What is the minimum power required to operate the pump?
ans:1.63kW

Given the inside and outside temperature, what is the Carnot efficiency of the pump?

Carnot efficiency = 1 - (Tc/Th) (h=hot temp., c=cold temp.)
 
about question1, I do not know the method. I have tried many times but the ans is not matched.
 
bennyngreal said:
about question1, I do not know the method. I have tried many times but the ans is not matched.

I think my method should work, are you sure that answer you posted is correct?
 
yes. This is my assignment needed to submit tomorrow. Please thanks
 
no.2 i still cannot prove the answer correct. I have used your calculation which is also my content of recent learning. But, I cannot do anything...
 
no ideas...oh my god
 
bennyngreal said:
no.2 i still cannot prove the answer correct. I have used your calculation which is also my content of recent learning. But, I cannot do anything...

For question 2, when you get the efficiency; you also know that efficiency = Heat/Work

so you can find the work like that.
 
May u write the procedure, thank you. If u are busy, it is not matter
 

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