   Chapter 12, Problem 64AP

Chapter
Section
Textbook Problem

A Carnot engine operates between 100°C and 20°C. How much ice can the engine melt from its exhaust after it has done 5.0 × 104 J of work?

To determine
The amount of ice that the engine can melt from its exhaust.

Explanation

Section1:

To determine: The energy exhausted.

Solution: the energy exhausted is 1.83×105J .

Explanation:

Given Info:

Temperature of hot reservoir of Carnot engine is 100°C .

Temperature of cold reservoir of Carnot engine is 20°C .

The work done by the engine is 5.0×104J .

Formula to calculate the exhausted energy from a heat engine is,

Qc=QhWeng

• Qh is the energy taken from the hot reservoir
• Weng is the work done by the engine

Thus,

Qc=WengeWeng=Weng(1e1) (I)

• e is the efficiency of the engine

For a Carnot engine, the efficiency is given by,

ec=1TcTh (II)

• Tc is the temperature of cold reservoir
• Th is the temperature of cold reservoir

Substitute equation (II) in (I),

Qc=Weng(ThThTc1)=Weng(TcThTc)

Substitute 5.0×104J for Weng , 100°C for Th and 20°C for Tc to find the exhausted energy Q

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