An automobile burns gasoline, producing gases at 2100 o C. The atmosphere is at

Question

An automobile burns gasoline, producing gases at 2100oC. The atmosphere is at 27oC.

a.) Find the efficiency of a Carnot engine operating between these temperatures.

b.) If this Carnot engine were to deliver 10 kW of usable power, what thermal power input would it require?

c.) The actual efficiency of automobile enginesis only 20 percent. When the losses in the drive train and transmission and the requirements of the lights, water pump, generator and other acessories are included, the overall system eficiency drops to about 12.5 percent. At what rate must energy be supplied by burning gasoline if the care requires 10 kW to overcome dissipative foces and maintain its speed?

Explanation / Answer

(a) Th= 2100 +273= 2373K

Tc = 27+ 273= 300k

efficiency= 1- Tc/Th

e= (1-300/2373) x 100

e= 87.4 %

(b) output power= 10 kw

let input power= Pi

e= output power/ input power

87.4% = 10Kw/ Pi

0.874= 10 Kw/ Pi => pi= 10Kw/0.874

so input power= 11.44 Kw

(c) efficiency= 12.5%

e= output power/ input power

output power required by car= 10 kw

12.5% = 10Kw/ Pi

0.125= 10 Kw/ Pi => pi= 10Kw/0.125

so input power= 80 Kw

so the burning gasolene has to provide 80 kW to keep car running.

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