He moved easily from the broad philosophical education of Glasgow University to the intensive mathematical training offered by Cambridge University, where he came second in the mathematics examination (the "Mathematics Tripos") in 1845. Having spent some weeks in Paris acquiring experimental skills in 1846 at the age of twenty-two, Thomson was elected to the Glasgow chair of natural philosophy which turned out to be a post that he held for fifty-three years.
Thomson married Margaret Crum in 1852. She died, childless, in 1870 after a very long illness that rendered her unable to walk. William's second marriage was to Frances Blandy in 1874. Again, there were no children. She outlived him.
Through the engineering influence of his older brother James, William became increasingly committed in the late 1840s to Sadi Carnot's theory of the motive power of heat. Since its somewhat obscure publication in 1824, Carnot's theory had become better known through its analytical reformulation ten years later by the French engineer Emile Clapeyron. The theory explained the action of heat engines by analogy to waterwheels. Just as a "fall" of water drove a waterwheel, so the "fall" of heat between the high temperature of the boiler and the low temperature of the condenser drove a steam engine.
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