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My race emigrated to a new world in approximately the 1600s. This world had no fossil fuels, but the race were gifted with many intelligent scientists who could discover new inventions.
The year is now 2015. What sort of inventions would these guys have?
Interestingly, this is slightly after the period where the British had developed coal mining to a very high art since they had reached "peak wood" in the late 1500's, and developed steam engines as a response to the need to pump water out of deep coal mines.
The real issue is the lack of high density energy in the form of carbon and hydrocarbons, which will be highly limiting. Portable engines for cars and airplanes will never be developed, and even regions where industrialization is possible will be limited to where renewable energy is cheap and common. The science of forestry will become highly developed, and large areas of land will be set aside for forestry, being harvested on decades long timelines.
Interestingly, nuclear energy is possible if the scientists can discover radioactivity or derive the idea from "fossil reactors" where uranium ore spontaneously fissioned. Stephen Baxter's book "Manifold Space" describes a very crude reactor where uranium rocks are piled together and moderated by long poles which have the ends charred. A very crude reactor like this is empirically possible by observing "fossil reactors" and can produce (radioactive) boiling water. Renaissance technology could produce a viable nuclear reactor capable of providing steam power, assuming the underlying principles were understood.
Electrical energy is also possible (people understood static electricity and even crude batteries), but the lack of large scale energy would be a bottleneck for producing copper wire, and this in turn would limit the development of technologies which require large scale use of electrical energy such as fixing nitrogen for fertilizer or making aluminum.
Overall, the world could have many of the innovations we take for granted, but on a much smaller scale and scope. The main lack would be transportation, limited to large vessels and vehicles which could carry steam engines and the large quantity of wood needed to fire the boilers.
Industrialization as we know it won't happen. Either population densities are lower or per-capita energy consumption is lower.
Global coal production is about 8 billion tons per year, or roughly one ton per person. Coal is roughly 10% of energy consumption, so if all other types could be replaced by coal the requirement would be 80 billion tons.
Since I'm guesstimating anyway, assume that coal can be replaced by an equal weight of charcoal. Finding the land use for charcoal production is difficult; all data is historical, but as a very rough guess call it 100 tons per square km per year. That would mean you need 800 million square miles of forest to get enough energy. Much more than the total land area of Earth.
That means you might have a genius inventer or a royal engineer, but the infrastructure to actually build those inventions won't be there.
While the other answers have concentrated on the alternative to fossil fuels as energy sources, there's another consideration if these resources didn't exist. Oil and its by-products play a large part in the manufacturing and engineering industries.
Without fossil oils, for example, you would have to find alternatives for making most plastics (and synthetic materials, such as nylon), alternatives for lubricating oils and an alternative for asphalt and tar on the roads. You'd even have to find another way of making chewing gum and lipstick.
I would hope that they'd be coming at renewable energy from the other direction to us, as the way for them to have a sustainable industrial revolution. On the other hand it's possible that wouldn't have happened, and quite likely that it won't happen for another century or few.
What won't have happened in that world is an industrial revolution based on steam engines, which make very inefficient use of combustion energy. With only wood and charcoal to use, steam won't replace water- and wind-mills as mechanical motive power, and the industrial revolution will be delayed.
What I hope will happen is that the values of the Enlightenment will still be at work, and scientific enquiry into the propreties of magnetic and electrical phenomena will find their Faraday, Maxwell, and Tesla and Edison. The electrical generator and the electric light-bulb and the lead-acid battery will be invented, the generators being powered by water-wheels and windmills, and later by water turbines and (small) dams. It will happen, given that prior to the light bulb, they don't even have gas-lights, just (vegetable) oil lamps and tallow candles.
Once they have utility electricity for lighting, low-powered electric gadgets will follow, and the spirit of scientific enquiry will start investigating what electricity is actually made of. Electric motors will give them vacuum pumps. The electron will be discovered. Then the thermionic valve, and radio.
Where I'm not so sure is whether they'll yet have scaled up hydro-power to large hydroelectric dams. The engineering princuples are obvious, but you'd have to burn a lot of trees to make enough concrete and iron rebar to build a large dam. That might hold things back until someone very rich was convinced that the huge investment was justified.
Meantime, in the research labs, will someone have found how to make a decent solar cell? That's their next key development, if they are to reach our level of technology. Once they can harvest sunlight without the inefficiencies of plantlife, they'll have all the electricity they can use. (The Earth's current electricity requirements could be satisfied by covering less than five percent of its deserts with solar panels). En route, they may have discovered solid-state electronics, but if they come at solar cells via chalcogenides or tellurides, maybe not yet. (These are easier than ultrapure silicon in a society with much higher energy costs than our own).
I don't think they'll have obtained practical nuclear power yet, unless their planet is younger than ours (naturally fissile Uranium without enrichment). Uranium enrichment requires prodigious amounts of electricity in, before you have enough sufficiently enriched uranium to get started. In our world, it was probably WW2 and the cold war which made nuclear power happen (as a side effect of making atomic bombs). In a lower-energy world, world wars would probably lie in their future not their past. (Mind you, small wars are no less deadly if you are fighting one).
