Premium gasoline produces 1.23×108 J of heat per gallon when it is burned at a temperature of approximately 400ºC (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 20.0ºC.
a) If your car gets 35.0 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?
b) Does it decrease or increase the entropy of the world?
ΔS = ΔSHOT + ΔSCOLD
The Attempt at a Solution
a) ΔS = ΔSHOT + ΔSCOLD
ΔS = -((.75*(1.23*108 J/gal)*(1 gal/35 mile)*(1 mile))/(400+273 K) + ((.75*(1.23*108 J/gal)*(1 gal/35 mile)*(1 mile))/(20+273 K)
ΔS = -3916 J/K + 8996 J/K
ΔS = 5079 J/K
b) Entropy increases (positive value for part a)
Would both ΔSHOT and ΔSCOLD be multiplied by .75, or would one be multiplied by the .25 efficiency?