When the first engines were designed there was no knowledge at all about the fundamentals of external combustion. When designers tried to improve the efficiency there was more and more need for a scientific basis of the processes in the engine. And it is there and then that the science of thermodynamics was developed. When the first theories were published there was no or little knowledge about atoms. Later on it shows that especially the behaviour of atoms is crucial for a good understanding of thermodynamic processes.

Never the less, in 1825 the French scientist Carnot published his theory about the maximum efficiency of ideal heat-engines.

He concluded that the efficiency is dependent on the relation between the temperature of the fresh steam and the temperature of the exhaust-steam. The formula was astonishing simple, the efficiency is (T_in - T_out) / T_out, all in oKelvin.

That is, the difference in temperature between fresh and exhaust steam, divided by the temperature of the fresh steam.

An engine working with fresh steam of 10 bar, with a temperature of 1700C or 443oK, and an exhaust of .5 bar (via a condenser), with a temperature of  80oC or 3530K, then the maximum efficiency is (443-353)/443 = 20%. And this for an ideal engine, so without any losses by heat-loss, internal resistance etc. To improve this efficiency you have to raise the temperature of the inlet-steam and/or reduce the temperature of the exhaust-steam. But with modern technology a maximum above 45% is not practically feasible.

The first Newcomen-engines reached no further than 1 percent efficiency, hypercritical modern electricity plants can get as far as 45%.

For the total equipment the efficiency of the boiler and piping is an extra factor. Most important loss is the chimney, at about 20% of the energy is lost via the chimney. So boilers, piping, internal resistance etc. can easily sum up to 30% of the fuel consumption. In case of an engine with a perfect efficiency of 20%, the total efficiency will be at about 14%.

The diagram below shows the development in steam-pressure and the consumption of fuel of the engines until 1900.