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

[bennyngreal]

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!

 

[rock.freak667]

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)

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 - (T_c/T_h) (h=hot temp., c=cold temp.)

 

[bennyngreal]

about question1, I do not know the method. I have tried many times but the ans is not matched.

 

[rock.freak667]

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?

 

[bennyngreal]

yes. This is my assignment needed to submit tomorrow. Please thanks

 

[bennyngreal]

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...

 

[bennyngreal]

no ideas...oh my god

 

[rock.freak667]

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.

 

[bennyngreal]

May u write the procedure, thank you. If u are busy, it is not matter