Convert BTU / pound to joule / kilogram
Learn how to convert
1
BTU / pound to
joule / kilogram
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{BTU}{pound}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{joule}{{\color{rgb(230,179,255)} kilo}gram}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{joule}{{\color{rgb(230,179,255)} kilo}gram}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{BTU}{pound}\right) = {\color{rgb(89,182,91)} \dfrac{1055.05585262}{0.5}\left(\dfrac{joule}{{\color{rgb(230,179,255)} kilo}gram}\right)} = {\color{rgb(89,182,91)} \dfrac{1055.05585262}{0.5}\left(\dfrac{J}{{\color{rgb(230,179,255)} k}g}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{joule}{gram}\right) = {\color{rgb(125,164,120)} 10^{3}\left(\dfrac{joule}{{\color{rgb(230,179,255)} kilo}gram}\right)} = {\color{rgb(125,164,120)} 10^{3}\left(\dfrac{J}{{\color{rgb(230,179,255)} k}g}\right)}\)
Define the values of the selected prefixes
\(\text{Right side: } \dfrac{1.0}{kilo} = \dfrac{1.0}{k} = {\color{rgb(204,139,6)} \dfrac{1.0}{10^{3}}}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{BTU}{pound}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{joule}{{\color{rgb(230,179,255)} kilo}gram}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1055.05585262}{0.5}} \times {\color{rgb(89,182,91)} \left(\dfrac{joule}{{\color{rgb(230,179,255)} kilo}gram}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(204,139,6)} \dfrac{1.0}{10^{3}}} \times {\color{rgb(125,164,120)} 10^{3}}} \times {\color{rgb(125,164,120)} \left(\dfrac{joule}{{\color{rgb(230,179,255)} kilo}gram}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1055.05585262}{0.5}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{J}{{\color{rgb(230,179,255)} k}g}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(204,139,6)} \dfrac{1.0}{10^{3}}} \times {\color{rgb(125,164,120)} 10^{3}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{J}{{\color{rgb(230,179,255)} k}g}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1055.05585262}{0.5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{J}{{\color{rgb(230,179,255)} k}g}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(204,139,6)} \dfrac{1.0}{10^{3}}} \times {\color{rgb(125,164,120)} 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{J}{{\color{rgb(230,179,255)} k}g}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1055.05585262}{0.5} = {\color{rgb(20,165,174)} x} \times 10^{3} \times \dfrac{1.0}{10^{3}}\)
\(\text{Simplify}\)
\(\dfrac{1055.05585262}{0.5} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{3}}{10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{3}}{10^{3}} = \dfrac{1055.05585262}{0.5}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{10^{3}}{10^{3}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{3}}{10^{3}} \times \dfrac{10^{3}}{10^{3}} = \dfrac{1055.05585262}{0.5} \times \dfrac{10^{3}}{10^{3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{3}}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}}{{\color{rgb(255,204,153)} \cancel{10^{3}}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = \dfrac{1055.05585262 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}{0.5 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1055.05585262}{0.5}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 2110.1117052\approx2.1101 \times 10^{3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{BTU}{pound}\right)\approx{\color{rgb(20,165,174)} 2.1101 \times 10^{3}}\left(\dfrac{joule}{{\color{rgb(230,179,255)} kilo}gram}\right)\)
