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At a pressure of one atmosphere methane boils at −161°C and freezes at −182.5°C. Consider a temperature scale where the boiling point of methane is 100.0°M and the freezing point is 0°M. Determine the temperature on the Methane scale that corresponds to the absolute zero point on the Kelvin scale. °M

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Answer:

[tex]-421.627906977\^{\circ}M[/tex]

Explanation:

Absolute zero in the Kelvin scale = -273.15 °C

Temperature difference in the boiling and freezing point

[tex]-161-(-182.5)=21.5\ ^{\circ}C[/tex]

Change in 21.5°C = Change of 100°C in M

[tex]1^{\circ}C=\dfrac{100}{21.5}=4.6511627907\ ^{\circ}M[/tex]

Difference in the Celsius scale

[tex]-182.5-(-273.15)=90.65\ ^{\circ}C[/tex]

Change in [tex]90.65\ ^{\circ}C[/tex] corresponds to

[tex]4.6511627907\times 90.65=421.627906977\ ^{\circ}M[/tex]

Therefore the absolute zero in the Methane scale is

[tex]-421.627906977\ ^{\circ}M[/tex]

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