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Well, unfortunately there are different BTUs, each a slightly different quantity of energy.

The BTU (ISO) is 1054.5 joules exactly. Let's use that one, and avoid some rounding.

10 kW = (10,000 joules/second) x (3,600 seconds/hour) x (1 BTU/1,054.5 joules) = 34,139.4 BTU/hour

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