A common mistake in textbooks of physics

A common mistake in textbooks of physics

The conventional method for calculating ideal thermal efficiency of internal combustion engines ought to be incorrect, because it neglects the transport work of exhaust process, and it obtains a higher efficiency than the right one.

For easily deducing, we will use the symbols in table 1.

§1 Thermodynamic Analysis

Example 1, the following is an extract from the page 678 of the textbook of “University Physics, by Young and Freedman, 12th edition” to describe the Otto cycle:


Note, the underline text above is problematic, because it neglects the transport work in the intake and exhaust stroke. This process for deducing expression (1), imitates the deduction of the Carnot cycle. However this regards the outside (cooling) cycle d-a of the Otto engine as equal to the inside cycle. This neglects the big difference between the gas cooled outside versus the gas cooled inside — the transport work.

For the ideal thermal efficiency of an Otto engine, we should consider the transport work in intake and exhaust process, and calculate it with expression (5).

§2 Enthalpy Analysis

We do enthalpy analysis on the Otto engine, seeing fig.3.

Reference expression (3) and (4), we obtain:

Comparing with expression (5), the results of expression (5) and (6) are the same.

§3 The Further

The ideal thermal efficiency by the expression (5) has less difference from the real thermal efficiency, and is simple to calculate. The expression (5) is a better ideal approaching of the real thermal efficiency than the expression (1).

In the “energy balance” experiment of an internal-combustion engine, we usually consider the energy lost from the exhaust by the enthalpy, which is the same as the deduction of the expression (6). And the results of expression (5) and (6) are the same. If we set the expression (5) as the formula of the ideal thermal efficiency of an Otto engine, then the whole thermodynamic system of internal-combustion engine becomes more coordinated.


Example 2, a gasoline engine, GM Saturn I4 1.9L DOHC, is an Otto engine, its compression ratio r=9.5, its measured best specific fuel consumption SFC=250g/(kW*h), so its measured best thermal efficiency e=0.33 or 33%. Comparison, the γ=1.4, we obtain its ideal thermal efficiency e=0.59 by expression (1), we obtain its ideal thermal efficiency e=0.43 by expression (5).

That difference between the result of the expression (1) and the measured value is bigger.

This difference between the result of the expression (5) and the measured value is smaller. This difference is 0.10. Thus, we estimate — The friction between the pistons and cylinder walls of the engine, consumes the mechanical work that comes from the expansion stroke which is about 20% of the engine’s output, it deducts 20%×0.33≈0.06 of thermal efficiency; The energy lost from the frictions of shafting, pumps, valve operation, etc., consumes the mechanical work that comes from the expansion stroke, deducts about 0.04 of thermal efficiency.


This mistake was found accidentally during our researching of the Zhou Engine.

Reference “Turbocharged Zhou Engine”, and based on — a) this difference between the result of the expression (5) and the measured value, mentioned above; b) Zhou Engine using of toothed-rollers, and avoiding nearly all the friction between the piston and cylinder of a conventional engine — we estimate that the difference between the ideal and the real thermal efficiency of Zhou Engine is less than 0.1 or 10%. The ideal thermal efficiency of the turbocharged Zhou Engine reaches to 0.74, which has deducted the transport work; we estimate that the real thermal efficiency will reach to 0.64 or 64%.

§4 Conclusion

Therefore, the ideal thermal efficiency of Otto cycle should be:

Similarly, the calculation for ideal thermal efficiency of Diesel engine should be altered.

As long as we know the better expression (5) for the ideal thermal efficiency calculation, we will be far easier to increase the real thermal efficiency. Even, we can invent some better internal-combustion engines


Note, the ideal thermal efficiencies of “Turbocharged Zhou Engine” and the patent are 0.74, which have considered the transport work.

Welcome comment, welcome share.

周经渊

发明“周引擎”,我正寻求合作伙伴和资金支持。

7 年

The deduction of this article, "If we are cooling the exhaust inside the exhaust pipe (of an IC engine), the transport work of the exhaust may reduce, and then the thermal efficiency may increase.", is very useful for cutting down carbon emission of the world. Volkswagen's 1.8L EA888 Turbocharged Engine has water-cooled exhaust, and its highway fuel consumption reduces about 20%. This example agrees with the deduction. Wish anybody to do more experimentation to verify the deduction.

周经渊

发明“周引擎”,我正寻求合作伙伴和资金支持。

7 年

The further researching shows “A Common Mistake in the Thermodynamics of Otto Engines” (https://www.dhirubhai.net/pulse/common-mistake-thermodynamics-ic-engines-jing-yuan-zhou ).

回复
Yogesh Kumar

Engine Systems Engineer at Aston Martin L.

7 年

Hi Jihua Zhou, it's interesting to see your interpretation of cycles. but, unfortunately you are not right. Instead of explaining the basics, I would like to suggest you to read the Chapter 5 of "Internal Combustion Engine Fundamentals by John B. Heywood. this book is considered as bible for Engine cycle calculations. It has all the answers of your doubts on real and ideal cycles, starting from most simple closed cycle to gas exchange, turbocharged and real cycles. Still, if you find it difficult to understand please let me know..

Jihua ZhouI guess I am missing your point here. Are you suggesting that we modify the calculation of efficiency in all idealized power cycles to account for transport work? Idealized cycles are idealized for a reason; they are systems (allow no mass transport across their boundaries) which are useful only for comparison with other idealized systems. Considering the transport work in any Control Volume analysis of a thermal power cycle will necessarily alter its calculated efficiency when compared with the idealized system as both Gonzalo and David have eluded to.

Gonzalo E. Meza

Project and Commercial Direction (Europe, LATAM, Africa and ME)

8 年

As far as I remember (and as the diagram shows), the ideal ("Carnot") efficiency is for a closed cycle (no intake or exhaust).

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