Answer
$1Btu=1054.87J$
Work Step by Step
Using the specific heat of water, we could write:
$1 Btu=1 lbs/F$
$4.186 J=1g/K$
Because $1lb=453.59g$: $1Btu=453.59g/F$.
Because a change of $1^{\circ}K$ equal to a change of $1.8^{\circ}F$: $1Btu=453.59g/F=\frac{453.59}{1.8}g/K\approx252g/K$
$1Btu=252g/K=252g/K*\frac{4.186J}{1g/K}\approx1054.87(J)$
