Fahrenheit or Celsius


Fahrenheit is such an odd American unit like square foot, pound or gallon. Or even worse: cubic foot, who has three feet? Nobody needs this crap any more and we should all switch to the metric system. Habits take a generation or two for this, but it will come… So now it is the metric system we should all strive for and of course Celsius degrees instead of Fahrenheit. Physics classes become a lot easier… Freezing of water at 0°C, boiling at 100°C. And the intermediate range is divided evenly and the scale is extrapolated to the top and the bottom. Quite simple, right?

Unfortunately not quite true. We have indeed introduced the metric system in most industrialized countries in many areas, but the temperatures have actually been excluded. The metric unit for temperature is Kelvin (K) and not °C. The next question is what an even subdivision of the temperature scale really means. Ok, the lines on the thermometer should have equal distances, but what liquid are we using for the thermometer?
What is the melting point and boiling point of water? Even slight quantities of dissolved substances and the air pressure have quite significant influence on them. But this can all be described and the temperature scale is precise enough for practical purposes. But the real thing is Kelvin (K).

If we are not using the metric system for temperatures anyway, we should ask, why. Everybody knows it: The Kelvin temperatures are clumsy and unintuitive. To some extent it is also just a matter of habit.

Most measurement units that we encounter in our daily life are used in a wide range of magnitudes. Lengths can be millimeters and thousands of kilometers, which is all really part of our daily life, not just some lab stuff. Times can be seconds and years. Masses can be milligrams and tons. When talking about temperatures we like to know the temperature of water and air and how it feels, most of the time. The melting point of aluminum is by itself interesting and maybe even useful to know when doing a chemistry or physics exam, but for most of us it is not really part of our daily life.

But for the feeling of temperatures and mapping of the relevant range the Fahrenheit scale is almost perfect:

  • A temperature difference of 1°C feels quite significant, but 0.1°C seem like exaggeration. 1°F might be a perfect step
  • The freezing point of water can be of some interest, for example in order to know if it is possible to go swimming in a lake or if icy highways can be expected. But some other temperatures need to be considered interesting: Down to about 0°F it is still quite ok with moderate clothing to move around outside. For much lower temperatures serious equipment is needed or it is good to keep the time outside really very short.
  • Our body temperature is near 100°F and temperatures up to this seem to be quite warm, but still bearable for a longer period of time for most of us. If it is warmer than that, it really gets way too hot for most of us. This is especially true for water temperatures.

It is unlikely that a switch from Celsius to Fahrenheit will ever happen in any country. But from all these non-metric unit Fahrenheit is the one that I consider most reasonable, much better than Celsius.

When working with temperatures in scientific context, especially in physical chemistry, the advantages of going all the way for metric units show up. Many formulas become much simpler when using Kelvin, not so much because of the scaling factor and more because of the fact that this ugly summand can be eliminated.

So the theoretical max of the efficiency of a temperature powered engine is \frac{T_1-T_2}{T_1} or the ideal gas formula is p \cdot v_m = R_m \cdot T (intensive form) or p \cdot V = n \cdot R_m \cdot T (extensive form). The intensive form abstracts from the quantity by using the volume per mol instead of the volume. Actually I prefer that, because the extensive forms imply an integration over the volume and a homogeneity, while intensive quantities describe matter at one point or a small vicinity of one point, as long as we can still abstract from the granularity due to the molecules and atoms. Measurements like temperature and pressure start to make sense with certain large number of molecules. Or what is the pressure or temperature of a single molecule?

For conversions between Fahrenheit, Celsius and Kelvin the following special values can help:

  • -40^{\rm o}{\rm C} = -40^{\rm o}{\rm F}
  • 0^{\rm o}{\rm F} = -17\frac{7}{9}^{\rm o}{\rm C}
  • 0^{\rm o}{\rm C} = 32^{\rm o}{\rm F}
  • 10^{\rm o}{\rm C} = 50^{\rm o}{\rm F}
  • 20^{\rm o}{\rm C} = 68^{\rm o}{\rm F}
  • 30^{\rm o}{\rm C} = 86^{\rm o}{\rm F}
  • 100^{\rm o}{\rm F} = 37\frac{7}{9}^{\rm o}{\rm C}
  • 100^{\rm o}{\rm C} = 212^{\rm o}{\rm F}

From these the conversion formulas can be deduced, but they are not so hard either:

  • k = \frac{5}{9}(f+ 459.67)
  • f = \frac{9}{5}k - 459.67
  • k = c + 273.15
  • c = k - 273.15
  • f = \frac{9}{5}c+32
  • c = \frac{5}{9}(f - 32)

k, f and c are the temperatures in K, °C and °F, respectively.

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