. 3. How does the efficiency compare with that of a Carnot engine operating betw
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. 3. How does the efficiency compare with that of a Carnot engine operating between the same two temperature extremes?Note: Figure neglects the intake of fuel-air and the exhaust of combustion products, which together involve essentially no net work. gamma , find the engine's efficiency, assuming all processes are reversible. 2.Find the maximum temperature in terms of the minimum temperature Gasoline engines operate approximately on the Otto cycle, consisting of two adiabatic and two constant-volume segments. The Otto cycle for a particular engine is shown in figure below. 1.If the gas in the engine has specific-heat rati . 3. How does the efficiency compare with that of a Carnot engine operating between the same two temperature extremes ?Note: Figure neglects the intake of fuel-air and the exhaust of combustion products, which together involve essentially no net work. gamma , find the engine's efficiency, assuming all processes are reversible. 2.Find the maximum temperature in terms of the minimum temperature Gasoline engines operate approximately on the Otto cycle, consisting of two adiabatic and two constant-volume segments. The Otto cycle for a particular engine is shown in figure below. 1.If the gas in the engine has specific-heat ratioExplanation / Answer
A.
? = 1 - 1/(r^k-1)
? = 1 - 1/V1/V2^?-1
? = 1 - 1 / [5^(?-1) ]
? = 1 - (5)^(1-?)
B. T3 in term of T1
Gas ideal equation,
PV = nRT
PV/T = nR = constant
P3V3/T3 = P1V1/T1
T3 = T1 * (P3/P1)* (V3/V1)
T3 = T1 * (P3/P1) /5
Solve for P3/P1,
P2V2/T2 = P1V1/T1
P1 = P2 * (T1/T2) * (V2/V1)
P1 = P2 * (T1/T2)/5
T3 = T1 * (P3/( P2 * (T1/T2)/5 ) /5
T3 = T1 * (P3/P2 / (T1/T2)
T3 = 3 T2
With, T2/T1 = (V1/V2)^?-1
thus, T3 = T1* 5^(?-1)
C,
Otto Efficiency
?_Otto = 1 - (5)^(1-?) or in term of temperature,
?_Otto = 1 - T1/T2
Carnot efficiency,
?_carnot = 1 - Tc/Th
?_carnot = 1 - T1/T3
Because T3 > T2, thus, T1/T3 < T1/T2, then ?_Otto < ?_Carnot
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