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20.28 Entropy Change Due to Driving. Premium gasoline produces 1.23×108Jof heat per gallon when it is burned at approximately 400°C(although the amount can vary with the fuel mixture). If a car’s engine is role="math" localid="1664272617143" 25%efficient, three-fourths of that heat is expelled into the air, typically at 20°C . If your car gets 35 miles per gallon of gas, by how much does the car’s engine change the entropy of the world when you drive 1.0 mi ? Does it decrease or increase it?

Short Answer

Expert verified

The car engine change the entropy of the world by S=3770.3J/K, and since it is positive, the entropy is increasing.

Step by step solution

01

Formula for change in entropy

Heat transport divided by temperature equals the change in entropy.

Entropy change in isothermal process is given by

S=QT

Here, S is the change in entropy, Q is the amount of heat, and T is the temperature.

02

Given data

Heat produced by gasoline when burned at 400°C,Q=1.23×108J/gallon,

Efficiency of car engine =25%

Car gets 35 miles per gallon of gas.

03

Calculate entropy change at  400°C

The car burns 1 gallon gasoline for 35 miles, therefore the burned heat

QH=Q×1mi35mi/gallon=1.23×108J/gallon×1mi35mi/gallon=3.5243×106J

Therefore, the entropy change at 400°C or 673.15K is define by,

SH=QHTH=3.5143×106673.15=5220.7J/K

04

Determine required entropy change

The car wastes the heat,

Qc=QH·1-Ef=3.5143×106.1-25100=2.6657×106J

Therefore, the entropy change at the car, at role="math" localid="1664273623096" 20°Cor293.15K is define as below.

SC=QCTC=2.6357×106293.15=8991.0J/K

Therefore, the entropy change is,

S=SC-SH=8991.0-5220.7J/K=3770.3J/K

Hence, the entropy is increasing.

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