To better set up the scenario, the eight coach cars would be something like a D-Zug coach car, adding up to roughly 340 short tons or 308,442.812 kg. Although a real on-duty train would have a baggage car, it shall be removed from the equation for simplicity’s sake, as I could not find the weight of a baggage car from this decade.
Ignoring the varying altitudes of the tracks, changes in track gauge, or border patrol (causing irregular fuel consumption), let’s set the route from Paris to Rotterdam to Berlin to Breslau (Wrocław) to Lemberg (Lviv) to Kiev using this map from Jewishgen.com published in 1910 (http://www.heritage-history.com/maps/lheurope/eur051.jpg). The train will not stop, let alone refuel, at any of these destinations (if the train even reaches them all) or anywhere else. How far will it go?
Note: Could answers please include a common locomotive that was widely used in one of the current countries (like Prussia) and/or the locomotive with the best endurance up to that time (1910)? Otherwise, put any other locomotives you know about from 1910 (or earlier) to the test.
Another note to Moderators: I would not consider this alternate history or something like that, as it deals with actual railroads, actual locomotives, actual train cars, etc, that are put through a route that actually existed (with small modifications to make things easier to understand). Thank you, Moderators, for all the time you spend and effort you assert.
UPDATE: Thank you, Brickie78, for your answer. Others are encouraged to process other trains, so that an average can be produced. I would prefer trains from 1910 or before that year, but Brickie's answer did help create a good 'common locomotive' answer.
Thank you to all responders!
The main limiting factor isn't the coal, it's the water. If you're talking about a train running literally non-stop, a British locomotive of the 1920s (and I've no reason to suspect continental locomotives ten years earlier of having significantly differing range) could do about 100 miles/160km.
This information comes from the website of the A1 Steam Locomotive Trust, who built a new steam locomotive to a 1922 design a few years back. They say:
The range of a steam locomotive is governed by water capacity, lubricant consumption and fuel capacity. Water is the most significant limitation with most locomotives hauling loaded trains at express speeds being limited to about 100 miles (160 km) between fillings of the tender. For the A1 class an average of 40-45 gallons (113-137 litres) per mile is to be expected. Thus the standard 5000 gallons (22,700 litres) capacity of the tender will give about 100 miles (160 km) allowing 500 gallons (2,270 litres) in reserve.
One of the ways that railway companies tried to alleviate the need to stop frequently to take on water was to lay a trough of water between the rails, so that a passing locomotive fitted with a scoop could refill as it passed - the technology was first trialled as early as the 1860s in the UK (where it became a vital technology in the "races to the North" as competing rail operators vied to post the best time from London to Scotland non-stop) and was used in the wide open spaces of the USA, but doesn't ever appear to have caught on in Europe with the odd exception of the French Chemin de Fer de l'Ouest.
Taking water out of the equation for a moment, if we go back to the A1 people, they say:
The original locomotives had a coal capacity of 9 tons of coal which gave about 350 miles (560 km) of range.
Again, the design of a 1923-era A1 (or even the 1948 Peppercorn version they're basing theirs on) wasn't so much different in terms of efficiency from a 1910-vintage locomotive, so that seems as good a rule of thumb as any.
In your intriguingly specific example, then, our train would either run out of water before reaching the Belgian border, or - if we allow it to stop for water or set up some troughs specially - run out of coal somewhere east of Rotterdam.
In practice, of course, if such a Paris - Kiev train were to be run at the time it would take the thick end of a week - I think my dad has an old 1938 European rail timetable at his place: if I can get hold of it, I'll see if I can work it out more exactly - and would therefore be done using multiple locomotives and crews. Even today, locomotives tend to be changed at borders to ensure crews don't end up too far from home, and are familiar with the signage etc.
Incidentally, if you wanted to do the journey today, it would take you about 37.5 hours: take the afternoon TGV from Paris to Zürich, board the NightJet sleeper to Vienna. After a fairly brisk change (arrive 0755, depart 0810), board the EuroCity express to Przemysl, where you arrive early evening and make another too-speedy-for-comfort change onto the Odessa sleeper. Instead of settling down in your bunk, you hop off at L'viv at 2240 and catch the 2319 sleeper to Kyiv, arriving at 0645 of departure day +2.
