The second industrial revolution was dependent upon the first.
The First Industrial revolution was about new manufacturing techniques which dramatically increased efficiency and concentrated production. It was about moving away from the master/apprentice manufacturing system and using lower skilled labor while dramatically increasing efficiency. Adam Smith in Wealth of nations used the example of pin manufacturing. One master pin craftsman performed 18 steps, straightening the wire, cutting the wire, pointing the pin, even folding the envelope in which he sold his pins, etc. Smith observed separating labor where multiple people were utilized each performing individual tasks did not just maintain production but dramatically increased it by multiple orders of magnitude. Thus one industrial manufacturing center using these techniques (specialized labor) could produce enough pins for a region. The more individual steps which could be defined, permitted more people to be added to the process; and the more efficient the process became. This all lead a need for increased international trade, and concentration of manufacturing.
Now each town didn't need a pin master craftsman one centralized manufacturing center could produce more pins at a lower expense than many towns required. The old craft system just could not compete. This also lead concentration of wealth as now manufacturing wasn't a subsistence endever but had the capability to yielding great sums of money. Smith's went on to say, the wealth of nations was defined in not the gold they possessed but how they spent the gold yielded by this new and more efficient manufacturing. That industries which invested their gold in continually improving manufacturing would survive and those which did not would be replaced by those who did. That the real wealth of nations was found in what they produced and was dependent on their ability to reinvest their profits.
The Second industrial Revolution which occurred 100 years latter involved utilization of new power sources. Oil and Electricity as well as new manufacturing science for steel. The second industrial Revolution relied on the first because first had
- concentrated manufacturing which enabled the more efficient adoption of the new power sources and materials;
- demonstrated the value/need to constantly seek out and improve production
- created an industrialists class who could afford to create and utilize these improvements
If there was no first industrial revolution and manufacturing remained distributed and a subsistence pursuit with no motivation to improve; it's less likely the second would have occurred. Even if the science was independently discovered, it would have been less likely to have been used without the lessons learned in the first.