The kelvin scale starts at the coldest temperature there is
Definition
Absolute zero
The lowest temperature that can exist, −273 ∘C-273\ ^\circ\text{C}−273 ∘C or 0 K0\ \text{K}0 K, at which the particles of a substance have the least kinetic energy they can possibly have.
- The Celsius scale puts its zero at the melting point of ice, which is a convenient choice but not a physically special one, and it allows temperatures below zero.
- The kelvin scale, also called the absolute scale, instead puts its zero at absolute zero, the point where there is no kinetic energy left to remove.
- Because nothing can be colder than absolute zero, no temperature in kelvin is ever negative.
- The two scales use steps of exactly the same size, so a rise of 1 K1\ \text{K}1 K is the same rise as 1 ∘C1\ ^\circ\text{C}1 ∘C and only the starting point differs.
- A kelvin temperature is written with the symbol K\text{K}K and no degree sign, so room temperature is 293 K293\ \text{K}293 K and never 293 ∘K293\ ^\circ\text{K}293 ∘K.
- The advantage of the absolute scale is that a kelvin temperature is directly proportional to the average kinetic energy of the particles, so doubling the kelvin temperature really does mean twice the average kinetic energy, which is not true of Celsius.
Converting between kelvin and degrees Celsius
Definition
Absolute (kelvin) temperature
The temperature measured from absolute zero upwards, in kelvin, related to the Celsius temperature by adding 273273273.
T=θ+273 T = \theta + 273 T=θ+273where TTT is the temperature in K\text{K}K and θ\thetaθ is the temperature in ∘C^\circ\text{C}∘C.
- To go from degrees Celsius to kelvin, add 273273273.
- To go from kelvin to degrees Celsius, subtract 273273273, which is the same equation rearranged to θ=T−273\theta = T - 273θ=T−273.
- Three values worth carrying in your head are 0 ∘C=273 K0\ ^\circ\text{C} = 273\ \text{K}0 ∘C=273 K, 100 ∘C=373 K100\ ^\circ\text{C} = 373\ \text{K}100 ∘C=373 K and −273 ∘C=0 K-273\ ^\circ\text{C} = 0\ \text{K}−273 ∘C=0 K.
- A temperature difference is the same number on both scales, so warming water from 20 ∘C20\ ^\circ\text{C}20 ∘C to 60 ∘C60\ ^\circ\text{C}60 ∘C is a rise of 40 ∘C40\ ^\circ\text{C}40 ∘C and also a rise of 40 K40\ \text{K}40 K.
- Adding 273273273 to a difference is therefore wrong, and only single temperatures get converted.
- A negative Celsius temperature still converts by adding, so −50 ∘C-50\ ^\circ\text{C}−50 ∘C becomes −50+273=223 K-50 + 273 = 223\ \text{K}−50+273=223 K.
Common Mistake
- Do not write a degree sign with kelvin, because the correct form is 300 K300\ \text{K}300 K and 300 ∘K300\ ^\circ\text{K}300 ∘K is marked wrong.
- Do not subtract when you mean to add: going up to kelvin always adds 273273273, and coming back down always subtracts it.
- Do not convert a temperature change, because a rise of 30 ∘C30\ ^\circ\text{C}30 ∘C is a rise of 30 K30\ \text{K}30 K, not 303 K303\ \text{K}303 K.
- Do not offer a negative kelvin temperature as an answer, because getting one means the arithmetic has gone wrong.
Exam technique
- You have to recall the conversion, so write T=θ+273T = \theta + 273T=θ+273 down before substituting; it costs a second and protects the working mark.
- Check every gas calculation for the phrase "in kelvin", since a gas question set up with Celsius values is the most common way marks vanish here.
- Sanity-check the answer: a kelvin value should come out larger than the Celsius value, and it should never be below zero.
- If a question asks why absolute zero is the lowest possible temperature, answer in terms of the particles having the least kinetic energy possible, not "because it is the coldest".
Self review
- State the value of absolute zero in degrees Celsius and in kelvin.
- Write the equation linking a kelvin temperature to a Celsius temperature.
- Convert 250 K250\ \text{K}250 K into degrees Celsius.
- Water is heated from 15 ∘C15\ ^\circ\text{C}15 ∘C to 75 ∘C75\ ^\circ\text{C}75 ∘C. What is the temperature rise in kelvin?
- Why can no object have a negative temperature in kelvin?
