How hot is it?

How hot is it?

Some years ago, I was perusing a book my then-preschooler had picked up at a thrift store. This ‘science for kids’ book was likely written by someone with a stronger background in kids’ books than science. The text was easy enough to read and understand, but the facts and concepts were lacking.

Though years have passed and I have forgotten much of what was in the book, one thing still stands out in my memory. The author, trying to convey the intense heat of the planet Venus, made the statement that Venus was over 800 degrees Fahrenheit (which is true)-twice as hot as an oven and over six times as hot as the highest temperature on Earth (which is not true). Here’s why:

People think of temperature in terms of hot and cold, but in reality heat is a quantifiable metric, while cold is not. You can have any amount of heat and still be able to add heat; the coldest condition is the complete lack of heat known as absolute zero-if cold was ‘something’, you could still add more ‘cold’ at that point. This is where the problem comes in.

Fahrenheit is not an absolute scale. There are temperatures below 0F, so the zero is a point within the range of possible temperatures (not at the beginning). So, if it is 40 degrees in Maine and 80 in Florida, it is not twice as hot (or cold) in one place than the other. The problem is easier to see if you consider the case where it is -10 in Duluth and 30 in Sioux Falls; how do they compare? Is it -3 times as warm in Sioux Falls? The only way to express a ratio of temperature is to use an absolute scale like Kelvin or Rankine.

In any absolute scale, the 0 point is absolute zero. From there, it does not matter how large your increments are, they still maintain the same relative ratios. For instance, if you compared the two main absolute scales, Kelvin (using the increments from Celsius and subtracting 273.15) and Rankine (using the increments from Fahrenheit and subtracting 459.67), you would see that 100K=180R and 200K=360R. So, double the heat in one absolute scale and you double the heat in any other (note that 100K or 100C is the difference between water freezing and boiling, as is 180R and 180F). If we do the same with Fahrenheit and Celsius, we see that 100C=212F and 200C=392F; Celsius doubled, but Fahrenheit did not. Using smaller numbers would exaggerate this effect, while using larger ones would make the difference between 0C/F and absolute zero less significant; 10C=50F, 20C=68F, doubling C increases F by 36 percent; 1000C=1832F, 2000C=3632F, doubling C increases F by 98.3 percent-nearly the same.

So why does this matter? For the most part, I am just being difficult. But also, it really doesn’t make sense, especially when dealing with negative temperatures. And though I understand that science needs to be watered down to reach its audience, I hate the thought of starting kids of with a wrong concept of how things work.

In the end, though, it really matters when doing calculations. Where corrections are done in an experiment based on differences in heat, the ratios have to be based on an absolute scale. If heat accelerates a reaction in a linear manner, doubling of heat needs to mean double the quantity of heat and not just a number on a thermometer if the data is to be reliable.