Cold day at work!

-2˚C = 271.15K.

The temperature tomorrow would then be 135.575K (which is half of 271.15K)

Converting that to Celsius (-137.575˚C) and rounding to the nearest integer, you get -138˚C.

For simplicity, let’s start at 10 °C. Someone with just enough knowledge to be dangerous would say that “twice as cold” would be 5 °C. Asking the same question in the USA where °F is used, we would start with 50 °F, and probably say that 25 °F is twice as cold.

Now, a relative coldness like we’re working with here should not depend on the scale we use to measure the temperature. “Twice as cold” in the USA where we use °F should also be “twice as cold” in the rest of the world where °C is used.

But 10 °C = 50 °F. And 5 °C = 41 °F. Yet for a USAan to answer that “twice as cold as 50 °F is 41 °F” would be ridiculous, right?

So the problem is that the temperature scales we commonly use, °C and °F, are useless for making quantitative comparisons. That is because they have arbitrary zero points. Or, putting it another way, negative temperatures are possible in both scales. The only way a quantitative comparison is possible is if, in your measurement scale, zero means zero. With temperature, that means using absolute temperatures like Kelvin.

Coming back to the question at hand, we know that °C + 273 = Kelvin (K), so, -2°C = 271 K

Now, the average kinetic energy of gas molecules (which determines hotness & coldness) is given by,

When it gets twice as cold, it means that the average kinetic energy of molecules drops to half, so the absolute temperature also drops to half, i.e. 135.5 K

And 135.5 K = (135.5 - 273)°C = -137.5°C or -138°C (rounded off)