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Celsius and kelvin

Heat and matter · level 4, lesson 1 of 6

A question to start

NASA's fact sheet gives Mars's average temperature as 214 K. What is a K, and is 214 hot or cold?

The idea

The Celsius scale is set by water: 0 °C where it freezes and 100 °C where it boils (at Earth's sea-level air pressure).

But there is a coldest possible temperature, where particles have the least energy they can have. It is absolute zero, −273.15 °C. Nothing can be colder.

The kelvin scale starts there. Its steps are the same size as Celsius degrees, so

\[T\ (\text{K}) = T\ (°\text{C}) + 273.15.\]

There is no degree sign: you write 214 K, "214 kelvin". In the United States, temperatures are often in Fahrenheit: \(T\ (°\text{F}) = 1.8\,T\ (°\text{C}) + 32\).

0 K−273 °C: absolute zero214 K−59 °C: Mars average 273 K0 °C: ice melts288 K15 °C: Earth average373 K100 °C: water boils
Temperatures Mars Earth
Average 214 K (−59 °C) 288 K (15 °C)

Worked examples

1. Mars to Celsius. \(214 - 273 = -59\) °C.

2. Body heat to kelvin. \(37 + 273 = 310\) K.

3. A change. Viking 1's site warmed from 184 K to 242 K: a rise of 58 K, which is also a rise of 58 °C.

4. To Fahrenheit. 20 °C is \(1.8 \times 20 + 32 = 68\) °F.

Try it

  1. Convert 0 °C to kelvin.
  2. Convert 300 K to °C.
  3. Can anything be at −300 °C? Why?
  4. Convert −40 °C to °F.
Answers
  1. 273 K.
  2. 27 °C.
  3. No. That is below absolute zero, −273.15 °C, the coldest possible.
  4. \(1.8 \times (-40) + 32 = -40\) °F. At −40 the two scales agree.

Common mistake

"Twice the temperature in °C means twice as hot." 20 °C is not twice as hot as 10 °C. Only in kelvin do ratios make sense: 293 K against 283 K, about 4% more.

Where it leads