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if a non - human civilization were to develop on saturns largest moon, titan, its scientists might well develop a temperature scale based on the properties of methane, which is much more abundant on the surface than water. methane freezes at - 182.6°c on titan, and boils at - 155.2°c. taking the boiling point of methane as 100.0°m (degrees methane) and its freezing point as 0°m, what temperature on the methane scale corresponds to the absolute zero point of the kelvin scale?
(there is an image showing the celsius scale and methane scale with markings: boiling point of methane at - 155.2 °c and + 100.0 °m, ice point of methane at - 182.6 °c and 0 °m, absolute zero at - 273.15 °c and? °m)
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Explanation:

Step1: Find the conversion formula

Let \(C\) be the temperature in Celsius, \(M\) be the temperature in Methane scale.
We know two points: \((C_1,M_1)=(- 182.6,0)\) and \((C_2,M_2)=(-155.2,100)\)
The slope \(m=\frac{M_2 - M_1}{C_2 - C_1}=\frac{100 - 0}{-155.2+182.6}=\frac{100}{27.4}\)
The equation of the line is \(M - M_1=m(C - C_1)\), so \(M=\frac{100}{27.4}(C + 182.6)\)

Step2: Substitute \(C=-273.15\)

Substitute \(C =-273.15\) into the equation \(M=\frac{100}{27.4}(-273.15 + 182.6)\)
First, calculate \(-273.15+182.6=-90.55\)
Then \(M=\frac{100\times(-90.55)}{27.4}\)
\(M=-330.5\)

Answer:

\(-330.5\)