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

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Homework Help Overview

The problem involves a Carnot engine operating between a hot reservoir of boiling water and a cold reservoir containing ice and water. The inquiry focuses on determining how much ice is melted when a specific amount of heat is added to the engine.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the efficiency of the Carnot engine and its implications for work output and heat transfer to the cold reservoir. There are questions about the calculations involving efficiency and the heat of fusion. Some participants explore the relationship between the heat input and the resulting melting of ice.

Discussion Status

The discussion includes various attempts to calculate the efficiency and the resulting work output. Some participants have provided guidance on using the efficiency to determine the heat delivered to the cold reservoir, while others are exploring the implications of the second law of thermodynamics in this context. There is an acknowledgment of the calculations leading to a specific amount of ice melted, although consensus on the approach has not been explicitly stated.

Contextual Notes

Participants are working within the constraints of a homework problem, which may limit the information available for discussion. The assumptions regarding the temperatures of the reservoirs and the state of the ice at the end of the process are also under consideration.

rlc
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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?
 
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rlc said:
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?
 
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).
 
Would the work output be the efficiency times the J heat put into the engine?
 
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!
 

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