The Kelvin Temperature Scale

The Kelvin scale is an absolute temperature scale. Zero kelvin (0 K) is absolute zero, the lowest possible temperature, where particles have the minimum possible kinetic energy.

Converting between Celsius and Kelvin

$T(\text{K}) = \theta(^\circ\text{C}) + 273$

Celsius	Kelvin
$-273$ $^\circ$C	0 K
0 $^\circ$C	273 K
100 $^\circ$C	373 K
25 $^\circ$C	298 K

A change of 1 K is the same size as a change of 1 $^\circ$C. The scales differ only in their zero point.

Why the Kelvin scale is needed

Gas law calculations require temperatures in kelvin. The Celsius scale has an arbitrary zero (the freezing point of water), which does not correspond to zero molecular kinetic energy. If you use Celsius in $pV = nRT$ or $\frac{p_1}{T_1} = \frac{p_2}{T_2}$, the proportionalities break down.

Absolute zero

At absolute zero (0 K):

• Particles have minimum kinetic energy.
• An ideal gas would have zero volume and zero pressure.
• It is impossible to cool anything below 0 K.

Worked example

Convert 37 $^\circ$C to kelvin.

$T = 37 + 273 = 310\text{ K}$

Convert 200 K to Celsius.

$\theta = 200 - 273 = -73\text{ }^\circ\text{C}$

Common errors and how to correct them

Using Celsius in gas law equations. Always convert to kelvin first. A temperature of 0 $^\circ$C is 273 K, not zero.

Writing the kelvin unit as “$^\circ$K.” The correct symbol is K, without a degree sign.

How to apply this in an exam

Convert all temperatures to kelvin before substituting into gas law equations. Show the conversion step explicitly to earn method marks.