7) A certain heat engine does 9.5 kJ of work and dissipates 8.00 kJ of waste hea

Question

7) A certain heat engine does 9.5 kJ of work and dissipates 8.00 kJ of waste heat in a cyclical process.

(a) What was the heat input to this engine?
kJ
(b) What was its efficiency?
%

8) The engine of a large ship does 2.20 108 J of work with an efficiency of 4.00%.

(a) How much waste heat is produced?
J
(b) How many barrels of fuel are consumed, if each barrel produces 6.00 109 J of heat when burned?
barrels

9) A 500 kg dragster reaches a speed of 110 m/s on level ground, starting from rest. Its efficiency is only 8.20% in producing kinetic energy, because of friction and its design for high power without regard to efficiency.

(a) How many gallons of fuel does it use during this acceleration, given there are 1.30 108 J of energy per gallon?
gal
(b) How much waste heat is produced?
J
(c) Once it is brought back to rest (assuming the engine shuts off at the end of the race), how much waste heat has been produced?
J

10) A certain gasoline engine has an efficiency of 36.0%. What would the hot reservoir temperature be for a Carnot engine having that efficiency, if it operates with a cold reservoir temperature of 180°C?
°C

Explanation / Answer

6. WORK DONE BY A CYCLE = AREA ENCLOSED BY THE CYCEL
Area enclosed by the cycle = (2 - 0.6)*(v2 - v1) + 0.5*(2.6 - 2)*(v2 - v1) - 0.5*(1 - 0.6)(V2 - V1)
now given, V1 = 2.5 *10^-3 , V2 = 10*10^-3
so, Area = 1.4*7.5*10^-3 + 2.25*10^-3 - 1.5*10^-3 = 11.25*10^-3 J
7. work done by engine, W = 9.5 kJ
energy dissipated by engine, D = 8 kJ
a) Input the engine = W + D = 17.5 kJ [ from conservation of energy]
b) efficienty = work done/heat addition = 9.5*10^3/(9.5*10^3 + 8*10^3) ) = 9.5/17.5 = 0.542857 * 100 = 54.285 %
8. work done by engine, W = 2.2*10^8
efficeiny of engine = 4 percent
so, 4/100 = (W)/(W + Q) [ Q is wasted heat]
25 = 1 + Q/W
Q = 24W = 24*2.2*10^8 = 5.28*10^9 J

number of barells of oil = 5.28*10^9/6*10^9 = 0.88 barrels

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