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.

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