Convert gallon atmosphere to watt • hour
Learn how to convert
1
gallon atmosphere to
watt • hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(gallon \text{ } atmosphere\right)={\color{rgb(20,165,174)} x}\left(watt \times hour\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(joule\right)\)
\(\text{Left side: 1.0 } \left(gallon \text{ } atmosphere\right) = {\color{rgb(89,182,91)} 460.63256925\left(joule\right)} = {\color{rgb(89,182,91)} 460.63256925\left(J\right)}\)
\(\text{Right side: 1.0 } \left(watt \times hour\right) = {\color{rgb(125,164,120)} 3.6 \times 10^{3}\left(joule\right)} = {\color{rgb(125,164,120)} 3.6 \times 10^{3}\left(J\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gallon \text{ } atmosphere\right)={\color{rgb(20,165,174)} x}\left(watt \times hour\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 460.63256925} \times {\color{rgb(89,182,91)} \left(joule\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \left(joule\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 460.63256925} \cdot {\color{rgb(89,182,91)} \left(J\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.6 \times 10^{3}} \cdot {\color{rgb(125,164,120)} \left(J\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 460.63256925} \cdot {\color{rgb(89,182,91)} \cancel{\left(J\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.6 \times 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(J\right)}}\)
\(\text{Conversion Equation}\)
\(460.63256925 = {\color{rgb(20,165,174)} x} \times 3.6 \times 10^{3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.6 \times 10^{3} = 460.63256925\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.6 \times 10^{3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.6 \times 10^{3} \times \dfrac{1.0}{3.6 \times 10^{3}} = 460.63256925 \times \dfrac{1.0}{3.6 \times 10^{3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.6}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.6}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = 460.63256925 \times \dfrac{1.0}{3.6 \times 10^{3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{460.63256925}{3.6 \times 10^{3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 460.63256925}{3.6}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.1279534915\approx1.2795 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(gallon \text{ } atmosphere\right)\approx{\color{rgb(20,165,174)} 1.2795 \times 10^{-1}}\left(watt \times hour\right)\)
