# Why is the change of temperature $\Delta T$ measured in Kelvins, degrees Celsius, etc.?

Let me start by apologizing if this question seems pedantic and say that I'm not very familiar with physics in general, as I'm a math major instead.

Anyway, say a body changes from temperature $T_1$ to $T_2$, with $T_2 \ge T_1$.

Then the change in temperature is $$\Delta T = T_2 - T_1$$

Now, it's clear that if $\Delta T = x\text{K}$ then $\Delta T = x \text{°C}$, with $x \ge 0$.

But it's also clear that $x \text{K} \ne x \text{°C}$, which leads to a contradiction.

Then I don't really understand why are units typically written in $\Delta T$? I suppose it could be to illustrate the units used to measure $T_1$ and $T_2$, but is it really necessary?

## 2 Answers

You need the units because though $x$ Kelvin is the same as $x$ Celcius it is not the same as $x$ Fahrenheit.

You can treat $\Delta T$ as a temperature. A temperature scale has a fixed zero point (absolute zero for the Kelvin scale and the freezing point of water for the Centigrade scale) and an interval defining 1 degree. To make $\Delta T$ a temperature you're just specifying that the fixed zero point is $T_1$, that is $\Delta T = 0$ when the temperature is $T_1$.

This may seem pedantic, but you would no doubt claim your height is six feet (or whatever it is). I'm sure you would not respond to a query by saying instead that the difference in height between the top of your head and the bottom of your feet is six feet.

• I see, so you can say $\Delta T = x$ Kelvin $= x$ Celsius, but this does not have the same meaning as saying a body has temperature $x$ Kelvin or Celsius, instead it's simply a way to specify the scale in which the change of temperature is measured, right? Thank you, by the way :) – Orlando Oct 22 '13 at 18:30
• Yes, just as saying your height is six feet defines the units without worrying where the zero point for the height scale is. – John Rennie Oct 22 '13 at 18:35

Units of temperature are K, degrees C, degrees F.

Units of temperature change are K, C degrees, and F degrees.