Absolute zero
Definition
Absolute zero
Absolute zero is the lowest temperature possible, at which the particles of a substance have the least kinetic energy they can have and stop moving.
- Cooling a substance reduces the average kinetic energy of its particles, so the particles move or vibrate more slowly.
- Kinetic energy cannot fall below zero, so there is a lowest possible temperature that no amount of further cooling can get past.
- At that temperature the particles have the least kinetic energy they can possibly have, so their movement effectively stops.
- This temperature is called absolute zero, and on the Celsius scale it is −273 ∘C-273\,^\circ\text{C}−273∘C.
- Nothing can be cooled below absolute zero, because there is no state of motion slower than no motion at all.
- A gas at absolute zero would exert no pressure, since particles that are not moving cannot collide with the walls of a container.
- Absolute zero has never been reached in practice, although research laboratories have cooled small samples to within a tiny fraction of a degree of it.
- The value of absolute zero is the same for every substance, because it describes the movement of particles rather than a property of one material.
The kelvin scale
Definition
Kelvin scale
The kelvin scale is the temperature scale whose zero is absolute zero and whose divisions are the same size as degrees Celsius.
- The kelvin scale starts at absolute zero, so 0 K0\ \text{K}0 K is the same temperature as −273 ∘C-273\,^\circ\text{C}−273∘C.
- A temperature in kelvin is never negative, because there is no temperature below absolute zero.
- The unit symbol is K\text{K}K and it is written without a degree sign, so a temperature is written as 300 K300\ \text{K}300 K.
- One kelvin is exactly the same size as one degree Celsius, so the two scales differ only in where their zero sits.
- A temperature change therefore has the same value on both scales, so a rise of 20 ∘C20\,^\circ\text{C}20∘C is also a rise of 20 K20\ \text{K}20 K.
- At atmospheric pressure water freezes at 273 K273\ \text{K}273 K and boils at 373 K373\ \text{K}373 K, and comfortable room temperature is about 293 K293\ \text{K}293 K.
- A kelvin temperature is called an absolute temperature, because it is measured from the true zero of particle movement.
- That is what makes the scale useful, because doubling the absolute temperature of a gas genuinely doubles the average kinetic energy of its particles, while doubling a Celsius reading does not.
Converting between the scales
- To convert from Celsius to kelvin, add 273273273, which gives T=θ+273T=\theta+273T=θ+273.
- To convert from kelvin to Celsius, subtract 273273273, which gives θ=T−273\theta=T-273θ=T−273.
- In these equations TTT is the temperature in kelvin and θ\thetaθ is the temperature in degrees Celsius.
- A negative Celsius temperature still converts to a positive kelvin value, so −40 ∘C-40\,^\circ\text{C}−40∘C becomes −40+273=233 K-40+273=233\ \text{K}−40+273=233 K.
- Convert individual temperatures but never convert a temperature difference, because a difference already has the same numerical value on both scales.
- Check the size of your answer as a quick test, since a kelvin value should always be larger than the Celsius value by 273273273.
Example
Converting Celsius into kelvin
- A gas is at a temperature of 30 ∘C30\,^\circ\text{C}30∘C.
- Using T=θ+273T=\theta+273T=θ+273 gives T=30+273T=30+273T=30+273.
- The temperature is T=303 KT=303\ \text{K}T=303 K.
- The same gas cooled to −18 ∘C-18\,^\circ\text{C}−18∘C would be at −18+273=255 K-18+273=255\ \text{K}−18+273=255 K.
Example
Converting kelvin into Celsius
- Liquid nitrogen boils at about 77 K77\ \text{K}77 K.
- Using θ=T−273\theta=T-273θ=T−273 gives θ=77−273\theta=77-273θ=77−273.
- The boiling point is θ=−196 ∘C\theta=-196\,^\circ\text{C}θ=−196∘C.
- The negative sign is expected here, because 77 K77\ \text{K}77 K is far colder than the freezing point of water.
Exam technique
Handling temperature scales
- Describe absolute zero using the movement of the particles, because a bare value of −273 ∘C-273\,^\circ\text{C}−273∘C answers only half of the question.
- Write the phrase least possible kinetic energy rather than no energy, which is the safer wording for a description mark.
- Show the addition or subtraction of 273273273 in your working, so a slip in arithmetic still leaves the method visible.
- Write K\text{K}K without a degree symbol, since the notation itself is sometimes credited.
- Read whether a question gives a temperature or a temperature change, because only a temperature needs converting.
Common Mistake
- Do not write 273 ∘K273\,^\circ\text{K}273∘K, because the kelvin scale uses no degree symbol.
- Do not subtract 273273273 when converting a Celsius temperature into kelvin, because the kelvin value is always the larger of the two numbers.
- Do not give a negative answer in kelvin, because it would describe a temperature below absolute zero.
- Do not add 273273273 to a temperature difference, because a change of 10 ∘C10\,^\circ\text{C}10∘C is a change of 10 K10\ \text{K}10 K.
- Do not claim absolute zero has been reached, because it can only be approached.
Self review
- State the value of absolute zero in degrees Celsius.
- Describe absolute zero in terms of the movement of particles.
- Convert 85 ∘C85\,^\circ\text{C}85∘C into kelvin.
- Convert 200 K200\ \text{K}200 K into degrees Celsius.
- Explain why a temperature in kelvin can never be negative.
- Explain why a temperature change has the same value in kelvin as in degrees Celsius.
