Convert (newton • meter) / hour to BTU / hour
Learn how to convert
1
(newton • meter) / hour to
BTU / hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{newton \times meter}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{BTU}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(watt\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{newton \times meter}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}\left(watt\right)} = {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}\left(W\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{BTU}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{1054.5}{3.6 \times 10^{3}}\left(watt\right)} = {\color{rgb(125,164,120)} \dfrac{1054.5}{3.6 \times 10^{3}}\left(W\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{newton \times meter}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{BTU}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(watt\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1054.5}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(watt\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(W\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1054.5}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(W\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(W\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1054.5}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(W\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{-7}}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1054.5}{3.6 \times 10^{3}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{10^{-7}}{{\color{rgb(255,204,153)} \cancel{3.6}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{1054.5}{{\color{rgb(255,204,153)} \cancel{3.6}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}}\)
\(\text{Simplify}\)
\(10^{-7} = {\color{rgb(20,165,174)} x} \times 1054.5\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1054.5 = 10^{-7}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1054.5}\right)\)
\({\color{rgb(20,165,174)} x} \times 1054.5 \times \dfrac{1.0}{1054.5} = 10^{-7} \times \dfrac{1.0}{1054.5}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1054.5}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1054.5}}} = 10^{-7} \times \dfrac{1.0}{1054.5}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-7}}{1054.5}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx9.4831673779 \times 10^{-11}\approx9.4832 \times 10^{-11}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{newton \times meter}{hour}\right)\approx{\color{rgb(20,165,174)} 9.4832 \times 10^{-11}}\left(\dfrac{BTU}{hour}\right)\)
