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 4.25×10−2 kg . Throughout this problem use Lf=3.34×105J/kg for the heat of fusion for water. A)During this time, how much work W is performed by the engine? W = ______________ J

Question
Asked Sep 18, 2019

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 4.25×10−2 kg .

 

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

 

A)

During this time, how much work W is performed by the engine?
 

W = ______________ J

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Step 1

The mass of ice is 4.25x10-2kg.

Write the expression for work done by heat engine.

(I)
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(I)

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Step 2

Write the expression for  and .

m is the mass ofice
L
isthe latent heat of fusion
Oc =-mL
substitute, 4.25x 10 kg for m
3.34x 10 J/kg for L
=-4.25x 10 kgx3.34 x10 J/kg
=-14.195 kJ
TH
=_
TC
=-(-14.195k 373K
273 K
=19.4kJ
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m is the mass ofice L isthe latent heat of fusion Oc =-mL substitute, 4.25x 10 kg for m 3.34x 10 J/kg for L =-4.25x 10 kgx3.34 x10 J/kg =-14.195 kJ TH =_ TC =-(-14.195k 373K 273 K =19.4kJ

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Step 3

Substitute the values of QH and QC i...

W - 19.4kJ-4.195 kj
= 5.2 kJ
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W - 19.4kJ-4.195 kj = 5.2 kJ

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