PSA- there’s no such thing as % temperature change (unless you’re working in K or R!)

Public service announcement- there is NO SUCH THING as a percent change in temperature, unless you happen to be working in absolute temperature units like Kelvin or Rankine degrees.  If you’ve using degrees Celsius or Fahrenheit, those are relative scales where values for 0 and 100 are arbitrarily pegged to physical phenomena (in the case of C to the freezing and boiling points of water, and in the case of F to the freezing point of brine and human body temperature, respectively, because English units are required to be even more stupidly arbitrary than SI units), and percent change in degrees C and degrees F will NOT be equivalent:

  • Start at 20 C (around room temperature)
    • this corresponds to [20*(9/5)]+32 = 68 F
  • Calculated a “10% temperature increase”
    • 20 C * 1.10 = 22 C
    • 68 F * 1.10 = 74.8 F
  • convert from Celsius back to Fahrenheit
    • [22*(9/5)]+32=71.6 F
  • Notice that 74.8 and 71.6 ARE NOT THE SAME
    • ZOMG!?!?

Because the Celsius and Fahrenheit scales based on differences compared to an arbitrarily-pegged zero point, it makes no sense to use them in percentages or ratios.  However, there are two equivalent temperature scales with degree units of the same size but where the zero point is set at absolute zero (as per the third law of thermodynamics) – the Kelvin scale (degrees K = degrees C +273.15) and the Rankine scale (degrees R = degrees F + 459.67).  In these units, you CAN talk about percentages and ratios and be self-consistent.  Here’s a more thorough example:

Screen Shot 2014-05-07 at 12.23.35 PM

Also, here‘s another discussion of the topic.  In short, if you talk about percent changes in temperatures in degrees C or F, you give the impression you have no idea what you are talking about.  This PSA is brought to you by this NBCNews article and the supplemental data section of this paper in the respected journal Environmental Research Letters (face-palm!!).

 

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