Convert BTU / hour to erg / minute
Learn how to convert
1
BTU / hour to
erg / minute
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{BTU}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{erg}{minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(watt\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{BTU}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{1054.35026444}{3.6 \times 10^{3}}\left(watt\right)} = {\color{rgb(89,182,91)} \dfrac{1054.35026444}{3.6 \times 10^{3}}\left(W\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{erg}{minute}\right) = {\color{rgb(125,164,120)} \dfrac{10^{-7}}{60.0}\left(watt\right)} = {\color{rgb(125,164,120)} \dfrac{10^{-7}}{60.0}\left(W\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{BTU}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{erg}{minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1054.35026444}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(watt\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10^{-7}}{60.0}}} \times {\color{rgb(125,164,120)} \left(watt\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1054.35026444}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(W\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10^{-7}}{60.0}} \cdot {\color{rgb(125,164,120)} \left(W\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1054.35026444}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(W\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10^{-7}}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(W\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1054.35026444}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-7}}{60.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-7}}{60.0} = \dfrac{1054.35026444}{3.6 \times 10^{3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{60.0}{10^{-7}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-7}}{60.0} \times \dfrac{60.0}{10^{-7}} = \dfrac{1054.35026444}{3.6 \times 10^{3}} \times \dfrac{60.0}{10^{-7}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{-7}}} \times {\color{rgb(99,194,222)} \cancel{60.0}}}{{\color{rgb(99,194,222)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{10^{-7}}}} = \dfrac{1054.35026444 \times 60.0}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancelto{10^{-4}}{10^{-7}}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1054.35026444 \times 60.0}{3.6 \times 10^{-4}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-4}}\text{ can be rewritten to }10^{4}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{4} \times 1054.35026444 \times 60.0}{3.6}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx175725044.07\approx1.7573 \times 10^{8}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{BTU}{hour}\right)\approx{\color{rgb(20,165,174)} 1.7573 \times 10^{8}}\left(\dfrac{erg}{minute}\right)\)
