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

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Homework Help Overview

The discussion revolves around calculating the minimum work input required to freeze 50 kg of water at 0ºC and the minimum power needed for a heat pump to maintain a house temperature of 22ºC while the outside temperature is -10ºC. The problem involves concepts of latent heat and thermodynamic efficiency.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the energy required for both freezing water and heating a house, mentioning the need to account for both sensible and latent heat. Questions arise about the methods used to arrive at the proposed answers and the calculations involved, particularly regarding the Carnot efficiency of the heat pump.

Discussion Status

Several participants express confusion about the methods to solve the problems, with some indicating that their answers do not match the proposed solutions. There is a mix of attempts to clarify the calculations and requests for procedural guidance, but no consensus on the correct approach has been reached.

Contextual Notes

Participants mention that this is an assignment due soon, which may add pressure to resolve the questions. There are indications of uncertainty regarding the correctness of the provided answers and methods.

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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