Carnot engine question help

Aug 2019
1
0
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/TH


Qin 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