Convert erg / hour to (newton • meter) / second
Learn how to convert
1
erg / hour to
(newton • meter) / second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{erg}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{newton \times meter}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(watt\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{erg}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}\left(watt\right)} = {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}\left(W\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{newton \times meter}{second}\right) = {\color{rgb(125,164,120)} 4.184\left(watt\right)} = {\color{rgb(125,164,120)} 4.184\left(W\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{erg}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{newton \times meter}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(watt\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 4.184}} \times {\color{rgb(125,164,120)} \left(watt\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(W\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 4.184} \cdot {\color{rgb(125,164,120)} \left(W\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-7}}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(W\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 4.184} \times {\color{rgb(125,164,120)} \cancel{\left(W\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{-7}}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times 4.184\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 4.184 = \dfrac{10^{-7}}{3.6 \times 10^{3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{4.184}\right)\)
\({\color{rgb(20,165,174)} x} \times 4.184 \times \dfrac{1.0}{4.184} = \dfrac{10^{-7}}{3.6 \times 10^{3}} \times \dfrac{1.0}{4.184}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{4.184}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{4.184}}} = \dfrac{10^{-7} \times 1.0}{3.6 \times 10^{3} \times 4.184}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-7}}{3.6 \times 10^{3} \times 4.184}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 10^{-7}}{3.6 \times 4.184}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-10}}{3.6 \times 4.184}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx6.639048226 \times 10^{-12}\approx6.639 \times 10^{-12}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{erg}{hour}\right)\approx{\color{rgb(20,165,174)} 6.639 \times 10^{-12}}\left(\dfrac{newton \times meter}{second}\right)\)
