Question

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?

Answer 1

Answer:
`-330.47 \°M`

Step-by-step explanation:

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

`\°C +273.15=K`

This means the absolute zero point of the Kelvin scale is
`0 K=-273.15 \°C`

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

Freezing point:
`0 \°M=-182.6 \°C=90.55 K`

Boiling point:
`100 \°M=-155.2 \°C=117.95 K`

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

`T=a+bt_(M)` (1)

Where:

`T` is the temperature in Kelvin

`t_(M)` is the temperature in degrees Methane

Firstly, we need to find the value of
`a` and
`b` with the two given points (
`90.55 K` and
`117.95 K`):

When
`T=90.55` and
`t_(M)=0`:

`90.55=a+b(0)`

`a=90.55` (2)

When
`T=117.95` and
`t_(M)=100`:

`117.95=90.55+b(100)`

`b=0.274` (3)

Now we have the linear equation:

`T=90.55+0.274t_(M)` (4)

Isolating
`t_(M)`:

`t_(M)=(T-90.55)/(0.274)` (5)

Evaluating for
`T=0 K`:

`t_(M)=(0-90.55)/(0.274)` (6)

Finally:

`t_(M)=-330.47 \°M`

This means
`0 K=-330.47 \°M`