If 100°C is equal to 212°F then why is 1°C not equal to (212/100) or 2.12°F but instead equal to 33.8°F?
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The scales for each is:
Celsius: 0°C freezing at sea level, 100°C boiling
Fahrenheit: 0°F freezing of brine, 96°F estimation of average human body temperature.
You can see from the start that there won’t really be a clean correlation or interoperability between the two, since their base units are so different.
Because steps between °F and °C is not the same : °C are design for freezing water at sea level at 0°C and boiling at 100°C. Farenheit is made up between random a cold day and a hot one for the 0-100, that’s why it’s so rubbich.
The zero point of the two scales is different. One is set at freezing point of pure water, and the other for a solution of ammonium chloride salt (-17°C).
Because scales are not the same, you use this formula to convert:
°C = (°F – 32) × 5/9 or
°F = (°C × 9/5) + 32
They have a linear relationship. Think of them as a line on a graph. Remember the formula for a line:
y = mx + b
Plug in the slope, 9/5, and the y intercept, 32, and you get:
y = 9/5x + 32
Or
y°F = 9/5x°C + 32
There’s a graph on this page:
https://www.wolframalpha.com/input?i=y%3D9%2F5x%2B32
You mistakenly assumed that 0 C = 0 F. That isn’t true. If it was, you’d be right: 1 C *would* be 2.12 F. But it isn’t.
0 C = 32 F. Why? The Celsius scale pegged 0 to the freezing point of water. The Fahrenheit scale didn’t.
What is the 0 point of the Fahrenheit scale pegged to, then? No one is really sure. Fahrenheit was a secretive sort. Some people say it’s the temperature of a certain brine solution, but that’s probably not why the zero point was chosen to be where it was. The brine solution was likely created after the fact to replicate that chosen temperature to calibrate newly made thermometers. It is most likely that the zero point was just “the temperature of some basement on the coldest day in winter” or something mundane like that.
Why such an arbitrary choice? Well, you have to give some credit to context here–this was still the era where negative numbers were considered loathesome to work with. They created pesky clerical errors in data recording and calculations. So in a pre-refrigeration tech society, pegging the zero point of your scale to the coldest possible natural temperature you’d expect to encounter to avoid negative numbers was an attractive idea.
Celsius and Fahrenheit have their zero points in different places. That means you can’t convert between them by multiplying by some number, as you can do with, say, pounds and kilos. The zeros for the two scales are 32°C apart and a degree Celsius is 9/5 of a degree Fahrenheit, so that gives the formula for conversion from Celsius to Fahrenheit as °F = (9/5)°C + 32. So a temperature of 1°C is 33.8°F.
But if you are talking about a *change* of 1°C, then there is a fixed conversion factor: the 9/5 in the formula above. A change of 1°C is a change of 1.8°F.
As for why the zeros of the two temperature scales are different, that’s down to history. Celsius set 0 and 100 degrees at the freezing and boiling points of water, respectively, while Fahrenheit set 0 at the considerably lower freezing point of salt water, the coldest temperature he could make, and 96 at body heat (which he got a little off). That range is easier to divide up into equal degrees than a range of 0 to 100.
Hey. Suppose you want to know how long is a thing. What you will do? You will find something straight, better if it is a ruler. Something straight with a length. That will be your *standard*.
You see, measuring the length of a thing is essentially comparing the measured thing with the standard. You may say a tree is roughly three times as high as you. Your height is the standard. If you think it is too sloppy, you will divide your standard into equal, smaller lengths. Now you can do a *finer* measurement. That is the *scale* on your standard. And this is how a ruler is made.
It is the same logic for measuring temperature. You need *two points* of temperature for an abstract “length”. That will be your standard to compare. And you divide your standard into equal, smaller parts.
Now you want to compare two rulers with two different scales. You need a common length enclaved on the two rulers, then you aligned the rulers with two endpoints of the common length. Only by then can you compare the length of the finer scales. You will not find the common length by a single point, there must be two points, right?
You may frown. Okay, we talk about the case directly. In the two temperature “rulers”, the 0°C is aligned with 32°F and the 100°C is aligned with 212°F. So the common “length” on the °C ruler is 100°C. But on the °F ruler, it is (212-32)=180°F. Thus the “length” of 1°C is 9/5°F and 1°F is 5/9°F.
There was extra trouble the past people made. Measuring temperature is something different from measuring length. When you use rulers, the usually used point with a “0” mark is your *reference point*. And you usually use the point to align one end of the measured thing. You will not causally put the point anywhere. But in temperature systems, the reference point can be aligned with any possible temperature. 0°C is not 0°F, but 32°F. 0°F is not 0°C, but -17.78°C. Hence it does not make sense to say directly “1°C = 9/5°F” because their reference points are not aligned with one temperature in reality.
The story ends here. Ah, no. I lied. Measure temperature as length is not “abstract” at all. We measured some length for it before. That was how (one kind of) thermometer works before!
They put some liquid into a glass tube. If it is hotter, the liquid will expanse and climb up in the tube. If it is colder, the liquid will contract and fall along the tube. As long as the liquid moves at a uniform speed for your stable heat source, that system will be a good thermometer. We just needed to measure the height of the liquid in the tube. Decades ago, this kind of thermometer (with mercury in the glass) was still quite common.
The Swedish astronomer Anders Celsius used the freezing point of the water as the reference point and the boiling point as the other point. Because he used water for his thermometer (If I am not wrong). And he subdivided the height difference into 100 parts. The two temperature points are exactly the points his thermometer fails. Since he used water, Celsius’s thermometer could not be sealed, that would be too dangerous. Vapors will explode. However, the speed of water flowing in the tube was thus quite sensitive to the air’s pressure.
The later German physicist Daniel Gabriel Fahrenheit had another idea. He made the mercury thermometer. It could be sealed, worked well, and could measure a wide range of temperatures. But the points he used for his standard were (1) the freezing point of a kind of salt solution (as the reference point) and (2) the average human body temperature at that time. And he subdivided the height difference into 90 parts. He did this for commercial considerations; the standard points he used were also quite useful in his age and he had the finest scale among different scales used at the day. He made his success once, but that becomes a troublesome legacy.
Most units you are familiar with have an obvious and universal zero point. For example, for mass the zero point is “weighs nothing”, and it is zero pounds, zero kilograms, zero ounces etc. no matter what unit you use. And that common zero is the reason why the conversion between, say, inches and centimeters is a simple proportionality. 1in = 2.54cm, 100in = 254cm and so on.
The zero point of temperature isn’t that obvious, and in the time of Fahrenheit, people didn’t even know for sure that such a point exists. That’s why the Fahrenheit and Celsius scales both use (different) arbitrary points, which could be reliably reproduced, as zeros.
There are temperature scales that use absolute zero as their zero point; Kelvin and Rankine, and there, the conversion again works just like you’d expect.
For every 100 units on celsius scale
You got 180 units on Fahrenheit
That’s what causes this difference
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