Convert thermie to gallon atmosphere
Learn how to convert
1
thermie to
gallon atmosphere
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(thermie\right)={\color{rgb(20,165,174)} x}\left(gallon \text{ } atmosphere\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(joule\right)\)
\(\text{Left side: 1.0 } \left(thermie\right) = {\color{rgb(89,182,91)} 4.1868 \times 10^{6}\left(joule\right)} = {\color{rgb(89,182,91)} 4.1868 \times 10^{6}\left(J\right)}\)
\(\text{Right side: 1.0 } \left(gallon \text{ } atmosphere\right) = {\color{rgb(125,164,120)} 383.5568490138\left(joule\right)} = {\color{rgb(125,164,120)} 383.5568490138\left(J\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(thermie\right)={\color{rgb(20,165,174)} x}\left(gallon \text{ } atmosphere\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 4.1868 \times 10^{6}} \times {\color{rgb(89,182,91)} \left(joule\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 383.5568490138}} \times {\color{rgb(125,164,120)} \left(joule\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 4.1868 \times 10^{6}} \cdot {\color{rgb(89,182,91)} \left(J\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 383.5568490138} \cdot {\color{rgb(125,164,120)} \left(J\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 4.1868 \times 10^{6}} \cdot {\color{rgb(89,182,91)} \cancel{\left(J\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 383.5568490138} \times {\color{rgb(125,164,120)} \cancel{\left(J\right)}}\)
\(\text{Conversion Equation}\)
\(4.1868 \times 10^{6} = {\color{rgb(20,165,174)} x} \times 383.5568490138\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 383.5568490138 = 4.1868 \times 10^{6}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{383.5568490138}\right)\)
\({\color{rgb(20,165,174)} x} \times 383.5568490138 \times \dfrac{1.0}{383.5568490138} = 4.1868 \times 10^{6} \times \dfrac{1.0}{383.5568490138}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{383.5568490138}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{383.5568490138}}} = 4.1868 \times 10^{6} \times \dfrac{1.0}{383.5568490138}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{4.1868 \times 10^{6}}{383.5568490138}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx10915.722169\approx1.0916 \times 10^{4}\)
\(\text{Conversion Equation}\)
\(1.0\left(thermie\right)\approx{\color{rgb(20,165,174)} 1.0916 \times 10^{4}}\left(gallon \text{ } atmosphere\right)\)
