A Carnot heat engine uses a hot reservoir consisting of a large amount of boilin

Question

A Carnot heat 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. In 5 minutes of operation of the engine, the heat rejected by the engine melts a mass of ice equal to 4.05×102 kg .

Throughout this problem use Lf=3.34×105J/kg for the heat of fusion for water.

A Carnot heat 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. In 5 minutes of operation of the engine, the heat rejected by the engine melts a mass of ice equal to 4.05×102 kg .

Throughout this problem use Lf=3.34×105J/kg for the heat of fusion for water.

Explanation / Answer

then what should i find with this problem

if you need a total work then following is the process

The heat transferred to the cold reservoir is:
Qc = &DeltaHf · m
= 3.34×105J/kg · 4.05×102 kg
= 13527J

The efficiency of a Carnot cycle is determined by the absolute temperature of the hot and the cold reservoir :
= 1 - Tc/Th
= 1 - 273K / 373K
= .2681

The efficiency is defined as unit work extracted from per unit heat transferred to the process:
= W / Qh
<=>
W = ·Qh

Conservation of energy requires that the amount oh heat transferred to process is equal to work done plus heat rejected:
Qh = W + Qc:

Therefore
W/ = Qc + W
=>
W = Qc / (1/ - 1)
= 13527J / (1/0.2681 -1) = 4955J

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