Convert BTU / cubic foot to BTU / cubic mile
Learn how to convert
1
BTU / cubic foot to
BTU / cubic mile
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{BTU}{cubic \text{ } foot}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{BTU}{cubic \text{ } mile}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{joule}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{BTU}{cubic \text{ } foot}\right) = {\color{rgb(89,182,91)} \dfrac{1054.5}{2.8316846592 \times 10^{-2}}\left(\dfrac{joule}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1054.5}{2.8316846592 \times 10^{-2}}\left(\dfrac{J}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{BTU}{cubic \text{ } mile}\right) = {\color{rgb(125,164,120)} \dfrac{1054.5}{4168181825.44058}\left(\dfrac{joule}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{1054.5}{4168181825.44058}\left(\dfrac{J}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{BTU}{cubic \text{ } foot}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{BTU}{cubic \text{ } mile}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1054.5}{2.8316846592 \times 10^{-2}}} \times {\color{rgb(89,182,91)} \left(\dfrac{joule}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1054.5}{4168181825.44058}}} \times {\color{rgb(125,164,120)} \left(\dfrac{joule}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1054.5}{2.8316846592 \times 10^{-2}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{J}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1054.5}{4168181825.44058}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{J}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1054.5}{2.8316846592 \times 10^{-2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{J}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1054.5}{4168181825.44058}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{J}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1054.5}{2.8316846592 \times 10^{-2}} = {\color{rgb(20,165,174)} x} \times \dfrac{1054.5}{4168181825.44058}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{1054.5}}}{2.8316846592 \times 10^{-2}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1054.5}}}{4168181825.44058}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{4168181825.44058} = \dfrac{1.0}{2.8316846592 \times 10^{-2}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{4168181825.44058}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{4168181825.44058} \times \dfrac{4168181825.44058}{1.0} = \dfrac{1.0}{2.8316846592 \times 10^{-2}} \times \dfrac{4168181825.44058}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{4168181825.44058}}}{{\color{rgb(99,194,222)} \cancel{4168181825.44058}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 4168181825.44058}{2.8316846592 \times 10^{-2} \times {\color{rgb(255,204,153)} \cancel{1.0}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{4168181825.44058}{2.8316846592 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 4168181825.44058}{2.8316846592}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx1.47197952 \times 10^{11}\approx1.472 \times 10^{11}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{BTU}{cubic \text{ } foot}\right)\approx{\color{rgb(20,165,174)} 1.472 \times 10^{11}}\left(\dfrac{BTU}{cubic \text{ } mile}\right)\)
