Convert BTU / cubic mile to BTU / liter
Learn how to convert
1
BTU / cubic mile to
BTU / liter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{BTU}{cubic \text{ } mile}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{BTU}{liter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{joule}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{BTU}{cubic \text{ } mile}\right) = {\color{rgb(89,182,91)} \dfrac{1055.05585262}{4168181825.44058}\left(\dfrac{joule}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1055.05585262}{4168181825.44058}\left(\dfrac{J}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{BTU}{liter}\right) = {\color{rgb(125,164,120)} 1.0545 \times 10^{6}\left(\dfrac{joule}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 1.0545 \times 10^{6}\left(\dfrac{J}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{BTU}{cubic \text{ } mile}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{BTU}{liter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1055.05585262}{4168181825.44058}} \times {\color{rgb(89,182,91)} \left(\dfrac{joule}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0545 \times 10^{6}}} \times {\color{rgb(125,164,120)} \left(\dfrac{joule}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1055.05585262}{4168181825.44058}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{J}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0545 \times 10^{6}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{J}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1055.05585262}{4168181825.44058}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{J}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0545 \times 10^{6}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{J}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1055.05585262}{4168181825.44058} = {\color{rgb(20,165,174)} x} \times 1.0545 \times 10^{6}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.0545 \times 10^{6} = \dfrac{1055.05585262}{4168181825.44058}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.0545 \times 10^{6}}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.0545 \times 10^{6} \times \dfrac{1.0}{1.0545 \times 10^{6}} = \dfrac{1055.05585262}{4168181825.44058} \times \dfrac{1.0}{1.0545 \times 10^{6}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.0545}} \times {\color{rgb(99,194,222)} \cancel{10^{6}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.0545}} \times {\color{rgb(99,194,222)} \cancel{10^{6}}}} = \dfrac{1055.05585262 \times 1.0}{4168181825.44058 \times 1.0545 \times 10^{6}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1055.05585262}{4168181825.44058 \times 1.0545 \times 10^{6}}\)
Rewrite equation
\(\dfrac{1.0}{10^{6}}\text{ can be rewritten to }10^{-6}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-6} \times 1055.05585262}{4168181825.44058 \times 1.0545}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx2.4003922243 \times 10^{-13}\approx2.4004 \times 10^{-13}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{BTU}{cubic \text{ } mile}\right)\approx{\color{rgb(20,165,174)} 2.4004 \times 10^{-13}}\left(\dfrac{BTU}{liter}\right)\)
