How did the industrial revolution lead to the cold war

The Industrial Revolution was the catalyst for the ideological divide between capitalism and communism that became the background of the Cold War.  Industrialization was fueled by capitalist economies and free markets.  The communist ideas of Karl Marx and Friedrich Engels arose as a criticism of capitalism, and as a plan for an industrialized world in which the people themselves owned the means of production and benefited from the full value of their labors.  The Soviet Union (the USSR) came into being as a result of communist revolution in Russia, and the USSR would become the great ideological enemy of the world's greatest capitalist power, the United States.

Another approach to this question would be that the Industrial Revolution led to the emergence of all sorts of new technologies -- including those applied to the waging of war.  The World Wars saw a tremendous advance in weaponry and technology for warfare, and tensions between nations escalated.  The development of atomic bombs were a further application of industrial technology, and they became the feared weapons held by both superpowers in a stand-off in the Cold War.