How much ice is melted in a Carnot engine using a hot and cold reservoir?

[rlc]

Homework Statement

A Carnot engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. When 6437 J of heat is put into the engine and the engine produces work, how many kilograms of ice in the tub are melted due to the heat delivered to the cold reservoir?

Homework Equations

Q=m*(deltaHf)
efficiency=1-(T_cold/T_hot)

The Attempt at a Solution

Searching online, I found those equations but nothing is working for me.
With the efficiency, I found:
1-(273/373)=0.268
And the heat of fusion for water is 3.34E5 J/kg

What am I missing?

 

[haruspex]

With the efficiency, I found:
1-(273/373)=0.268
And the heat of fusion for water is 3.34E5 J/kg

Given the efficiency and the quantity of heat input, how much work is output? How much heat is left to go into the cold reservoir?

 

[rude man]

You know T1 and T2 and Q1. Using zero universe entropy change as your criterion you can figure out Q2 and then of course the amount of ice meltred. Assume there is still ice left at T2 when the process ends (T2 is constant = 273K).

 

[rlc]

Would the work output be the efficiency times the J heat put into the engine?

 

[rlc]

Aha! I figured it out!
100-26.8% = 73.2%--of the added energy should be delivered as heat to the cold reservoir.
deltaH=m(Lf)
(0.732)(6437J)=m(3.34E5J/kg)
m=0.0141 kg ice melted

Thank you both for helping me!