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Physics / Physics: Principles with Applications 6 / Chapter 15 / Problem 44P

Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli

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Answer: A real heat engine working between heat reservoirs

Chapter 15, Problem 44P

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QUESTION:

Problem 44P

A real heat engine working between heat reservoirs at 970 K and 650 K produces 550 J of work per cycle for a heat input of 2200 J. (a) Compare the efficiency of this real engine to that of an ideal (Carnot) engine. (b) Calculate the total entropy change of the universe per cycle of the real engine. (c) Calculate the total entropy change of the universe per cycle of a Carnot engine operating between the same two temperatures.

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QUESTION:

Problem 44P

A real heat engine working between heat reservoirs at 970 K and 650 K produces 550 J of work per cycle for a heat input of 2200 J. (a) Compare the efficiency of this real engine to that of an ideal (Carnot) engine. (b) Calculate the total entropy change of the universe per cycle of the real engine. (c) Calculate the total entropy change of the universe per cycle of a Carnot engine operating between the same two temperatures.

ANSWER:

Solution 44P

Step 1 of 3

Part a

We required to compare the ideal and real engine efficiencies of the given heat engine.

Given:

The work produced $W=550$ J

The heat input $Q{\ }_{H}=2200$ J

The efficiency of the real engine,

$e{\ }_{real}=\frac{W}{Q{\ }_{H}}$

$e{\ }_{real}=\frac{550}{2200}$

$e{\ }_{real}=0.25$

Given:

The high temperature $T{\ }_{H}=970$ K

The low temperature $T{\ }_{L}=650$ K

Therefore, the ideal engine efficiency,

$e{\ }_{ideal}=1-\frac{T{\ }_{L}}{T{\ }_{H}}$

$e{\ }_{ideal}=1-\frac{650}{970}$

$e{\ }_{ideal}=0.33$

Therefore, if we compare the real engine efficiency to that of the ideal engine,

$\frac{e{\ }_{real}}{e{\ }_{ideal}}=\frac{0.25}{0.33}=0.76$

Therefore, the real engine efficiency is 0.76 times that of ideal engine efficiency.

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