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Q. 4.2

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An Introduction to Thermal Physics
Found in: Page 134
An Introduction to Thermal Physics

An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

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Short Answer

At a power plant that produces 1 GW109 watts) of electricity, the steam turbines take in steam at a temperature of 500o, and the waste heat is expelled into the environment at 20o(a) What is the maximum possible efficiency of this plant?(b) Suppose you develop a new material for making pipes and turbines, which allows the maximum steam temperature to be raised to 600o. Roughly how much money can you make in a year by installing your improved hardware, if you sell the additional electricity for 5 cents per kilowatt-hour? (Assume that the amount of fuel consumed at the plant is unchanged.)

a) Maximum possible efficiency of the plant = 62.1%

b) Money can be made in a year $ 30 million

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Part(a)- Step 1- Given Information

Temp at cold reservoir = 20o C and

Temp at hot reservoir = 500o

Pat(a)-Step 2- Explanation

Convert temp in K.

Tc =20o C = 273+20= 193 K

Th =500oC = 273+500=773 K

The efficiency of power plant is given as

e≤1-TcThSubstitute values,e≤1-293773e≤0.621

Maximum efficiency in percentage is 62.1%

Part(b)-Step 1- Given information

The temperature of the cold reservoir = 20oThe temperature of the hot reservoir = 600oThe power plant produces 109 watts of electricity that is 109 J/s.Rate of additional electricity is 5 cents /kwh.

Part(b)-Step 2 - Explanation

Th=600o=873 K and Tc=20o=293 K

Percentage of improved efficiency

1-293873(100%)=66.437%

With the improved efficiency the amount of electricity produced is

P=109×66.4462.1=1.0699×109 W

Padditional =0.0699×109 W=6.99107 W=6.99104 kW

If sold for 5 cents per kilo-watt-hour then the money made in one second is:

=104×6.99×53600 cents =97.083 cents

Money made in one year is

=97.083 x 3600 x 24 x 365 cents

=3,06,16,09,488 cents

covert in $

=$ 3,06,16,094.88

= $ 30 Million ( approx)

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