If a non-human civilization were to develop on saturn's 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?

Explanation:

Let's begin by explaining that the relation between the Celsius scale and Kelvin scale is:

This means the absolute zero point of the Kelvin scale is

Keeping this in mind, we have the freezing point and boling point of Methane as:

Freezing point:

Boiling point:

According to this, there is a linear relation between the methane scale () and the Kelvin scale in the form:

(1)

Where:

is the temperature in Kelvin

is the temperature in degrees Methane

Firstly, we need to find the value of and with the two given points ( and ):

When and :

(2)

When and :

(3)

Now we have the linear equation:

(4)

Isolating :

(5)

Evaluating for :

(6)

Finally:

This means

answer: 31, 5556. 952 seconds