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Thermodynamics  efficiency question 
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#1
May1406, 02:35 AM

P: 35

The burning of gasoline in a car releases about 3.0 x 10^4 kcal/gal. If a car averages 41 km/gal when driving 90 km/h, which requires 25 hp, what is the efficiency of the engine under those conditions?
I think I have an answer, but I'm not sure if it's correct. 1 horsepower = 746 watts 25 hp = 18650 watts 1 kcal = 4186 joules (watts / sec) e = W / Qh = 1  (Ql / Qh) 1 gal / 41 km at 91 km / h means that that 2.26 gallons will be used in one hour. Since no temperatues are given I don't think that the 1  Ql / Qh is needed... Converting 30000 kcal / gal to watts I get 34883 joules/sec. Since 2.26 gal are used, I multiplied the above by 2.26 to get 78836. Dividing 18650 watts (from hp) by 78836 I got an efficiency of 23.46%. 


#2
May1406, 05:46 AM

Sci Advisor
HW Helper
P: 6,654

You should state your answer algebraically so you and others can follow the physical reasoning. ie: [tex]\eta = W/Q_h = (dW/dt)/(dQ_h/dt)[/tex] Your answer is almost right. I get 2.195 gal/hr (90/41) not 2.26. [tex]dQ_h/dt = 2.195 * gal/hr = 3 x 10^4 * 2.195 * 4.186 KJ/hr = 2.76 x 10^8 J/hr = 7.66 x 10^4 J/sec[/tex] [tex]dW/dt = Power = 25 * 746 J/sec = 1.87 x 10^4 J/sec[/tex] So: [itex]\eta[/itex] = 1.87/7.66 = 24.4% AM 


#3
May1406, 05:55 AM

Emeritus
Sci Advisor
PF Gold
P: 9,781

I have not rigorously checked your answer, however the efficency appears reasonable for a car, just beware of rounding too early in your calculations, this could induce significant errors. For example you obtained 78836 watts for the input power of the engine, however I obtained [itex]78798\frac{2}{3}[/itex].
Just a small point that I sould point out is that here you said; ~H Sorry AM, didn't see your post. I sould learn to type faster 


#4
May1406, 04:14 PM

P: 35

Thermodynamics  efficiency question
Thank you.



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