How Much Water Can a 1KW Carnot Engine Freeze in 5 Minutes?

[zilex191]

Homework Statement

In a well-insulated refrigeration unit, a Carnot engine using an ideal gas is driven by a 1KW electric motor (80% efficient) to freeze water. Assuming that the temperature of the thermal sink is 20 °C, calculate the mass of water frozen in 5 minutes. Take the latent heat of water as 3.4 x 105 JKg-1

Relevant Equations

ncarnot = 1 -Qout/Qin = 1 - TL/TH
m = Q/L
W=Pt

Homework Statement: In a well-insulated refrigeration unit, a Carnot engine using an ideal gas is driven by a 1KW electric motor (80% efficient) to freeze water. Assuming that the temperature of the thermal sink is 20 °C, calculate the mass of water frozen in 5 minutes. Take the latent heat of water as 3.4 x 105 JKg-1
Homework Equations: ncarnot = 1 -Qout/Qin = 1 - TL/TH
m = Q/L
W=Pt

I've been stuck on this question for a long time ; here is what i have tried so far:

In a well-insulated refrigeration unit, a Carnot engine using an ideal gas is driven by a 1KW electric motor (80% efficient) to freeze water. Assuming that the temperature of the thermal sink is 20 °C, calculate the mass of water frozen in 5 minutes. Take the latent heat of water as 3.4 x 105 JKg-1

Formula for thermal efficiency:

ncarnot = 1 -Qout/Qin = 1 - TL/THQin i persume is given (20 °C) and ncarnot= 0.8 ; rearranging the formula you get Qout =100 °C

Wnet,out = Qout - Qin; Therefore Wnet,out = 80

at this point I'm lost, i know i need to find Q to fit into the formula m = Q/L as latent heat of water is given, but how do i combine the ncarnot with the latent heat formula+ time. Help will be much appreciated

The answer is supposed to be 9.6 kg

 

[Chestermiller]

80% is the motor efficiency, not the Carnot cycle efficiency.

 

[zilex191]

Ah ok thank you for your reply, so i use formula Output/input = 0.8, input into motor is 1000 W therefore output = 800 W

To work out energy transferred W=P x T ; W = 800 x (5minutes x 60) = 240000J

plug that into m= Q/L i get 0.71 kg.

Am i on the right track??

 

[Chestermiller]

Heat is removed from the water to form ice at the cold reservoir temperature of 0 C and transferred to the ideal gas at 0 C;, and a greater amount of heat is rejected from the ideal gas to the hot reservoir (sink) at 20 C. The difference between these two amounts of heat is the work done.