- #1

Tynged

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## Homework Statement

Premium gasoline produces

**1.23×10**of heat per gallon when it is burned at a temperature of approximately

^{8}J**400 ºC**(although the amount can vary with the fuel mixture). If the car's engine is

**25.0 %**efficient, three-fourths of that heat is expelled into the air, typically at

**20.0 ºC**.

__Part A:__If your car gets

**38.0 miles per gallon**of gas, by how much does the car's engine change the entropy of the world when you drive

**1.00 mile**?

__Part B:__Does it decrease or increase the entropy of the world?

## Homework Equations

[tex]\Delta S = S_2 - S_1 = \frac{Q}{T}[/tex]

Where [tex]\Delta S[/tex] is the change in entropy of the system, [tex]S_2[/tex] is the entropy of the system at its final state, [tex]S_1[/tex] is the entropy of the system at its initial state, [tex]Q[/tex] is the heat added to or removed from the system, and [tex]T[/tex] is the absolute temperature at which the process is occurring.

## The Attempt at a Solution

[tex]\Delta S = S_2 - S_1 = \frac{Q}{T} = \frac{(0.750)(1.23\times10^{8}\ J/gal)(1.00\ mi\times\frac{1\ gal}{38.0\ mi})}{673\ K} = 3610\ J/K[/tex]

I believe I went wrong when I used the temperature of the burning fuel mixture as the absolute temperature. I am sure the temperature of the surrounding air is also important somehow. Writing the equation for entropy differently, I tried to incorporate that second temperature.

[tex]\Delta S = S_2 - S_1 = \frac{Q_2}{T_2} - \frac{Q_1}{T_1} = \left(\frac{(0.750)(1.23\times10^{8}\ J/gal)(1.00\ mi\times\frac{1\ gal}{38.0\ mi})}{673\ K}\right) - \left(\frac{(0.250)(1.23\times10^{8}\ J/gal)(1.00\ mi\times\frac{1\ gal}{38.0\ mi})}{293\ K}\right)[/tex]

[tex]= 3610\ J/K - 2760\ J/K = 850\ J/K[/tex]

Although this seemed to be a step in the wrong direction because my first solution was closer to the correct answer according to the automatic response.

For Part B, I assume that driving the car will increase the entropy of the world since most processes I have seen naturally tend toward increasing disorder. I am sure the correct answer to Part A will be a positive change in entropy and support my assumption.

I would definitely appreciate any help you could offer. Thanks in advance!