Convert gallon atmosphere to BTU
Learn how to convert
1
gallon atmosphere to
BTU
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(gallon \text{ } atmosphere\right)={\color{rgb(20,165,174)} x}\left(BTU\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(joule\right)\)
\(\text{Left side: 1.0 } \left(gallon \text{ } atmosphere\right) = {\color{rgb(89,182,91)} 383.5568490138\left(joule\right)} = {\color{rgb(89,182,91)} 383.5568490138\left(J\right)}\)
\(\text{Right side: 1.0 } \left(BTU\right) = {\color{rgb(125,164,120)} 1054.5\left(joule\right)} = {\color{rgb(125,164,120)} 1054.5\left(J\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gallon \text{ } atmosphere\right)={\color{rgb(20,165,174)} x}\left(BTU\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 383.5568490138} \times {\color{rgb(89,182,91)} \left(joule\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1054.5}} \times {\color{rgb(125,164,120)} \left(joule\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 383.5568490138} \cdot {\color{rgb(89,182,91)} \left(J\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1054.5} \cdot {\color{rgb(125,164,120)} \left(J\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 383.5568490138} \cdot {\color{rgb(89,182,91)} \cancel{\left(J\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1054.5} \times {\color{rgb(125,164,120)} \cancel{\left(J\right)}}\)
\(\text{Conversion Equation}\)
\(383.5568490138 = {\color{rgb(20,165,174)} x} \times 1054.5\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1054.5 = 383.5568490138\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1054.5}\right)\)
\({\color{rgb(20,165,174)} x} \times 1054.5 \times \dfrac{1.0}{1054.5} = 383.5568490138 \times \dfrac{1.0}{1054.5}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1054.5}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1054.5}}} = 383.5568490138 \times \dfrac{1.0}{1054.5}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{383.5568490138}{1054.5}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.3637333798\approx3.6373 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(gallon \text{ } atmosphere\right)\approx{\color{rgb(20,165,174)} 3.6373 \times 10^{-1}}\left(BTU\right)\)
