Confused about when to convert units

Question

It shouldn't matter when I convert units in a calculation, the final answer should be the same. However:

$-30\ °C - 0\ °C = -30\ °C = (-30 + 273.15)\ K = 243.15\ K$

$-30\ °C - 0\ °C = (-30 + 273.15)\ K - (0 + 273.15)\ K = 243.15\ K - 273.15\ K = -30\ K$

where $T_C = T_K - 273.15\ K$, $C$ is Celsius, $K$ is Kelvin.

How come they're different?

Answer 1

A difference in temperatures isn't a temperature any more than a difference of dates is a date. You may convert temperatures to temperatures using your formula. Your formula does not convert differences in temperature to anything at all (in the same way that applying any other wrong conversion fails to produce a difference in temperatures).

Answer 2

The second is correct, and the first is incorrect. You're looking at the difference of two measurements (and the difference in Kelvin will be the same as the difference in Celsius). In your first line, you're making a difference into an absolute measurement and then converting it, and that is incorrect.

Answer 3

We have that

• $0 °C\equiv273.15 \,K$

and therefore for $T_C$ expressed in $°C$

• $T_K= T_C+273.15 $

therefore for $T_C=-30 °C$ we have

• $T_K=-30+273.15=243.15\,K$

and then

$$-30\,°C-0\,°C=-30\,°C=243.15 \,K-273.15 \,K=-30\, K$$

Answer 4

The reason why it doesn't matter when you convert units is because typical unit conversions are multiplicative ratios. For example,

1 m = 1000 mm

so

1 m/1000 mm = 1

And we know that we can multiple any term in an equation by 1 without changing the meaning of the equation. But as you can see in your example,

1 C= 1 K + 273.15 

the unit conversion for temperature is a shift, not a factor change. Clearly the difference is that in one equation you are introducing 273.15 once and in the other twice. For this reason the only time when you can convert between degrees Celsius and Kelvins is when the variable represents a difference like delta C or dC.

Answer 5

The addition or subtraction of 273.15 is not actually a unit conversion; it is a scale conversion.

As units of heat, 1 degree Celsius = 1 Kelvin (and also, 9/5 degree Fahrenheit).

Addition or subtraction enters the picture because when we measure actual temperatures, we do it relative to a base point that is different for each scale. When we say it is 30C outside, we really mean it is 30 degrees Celsius above the freezing point of water, which is another way of saying it is 303.15 degrees Celsius above absolute zero.

So if you have a temperature measured in the standard Celsius scale -- e.g. "it's 30C outside today" -- you would add 273.15 to convert it to Kelvin. But if you have simply a quantity of degrees Celsius -- e.g. "the temperature increased by 30C overnight" -- the quantity is exactly the same in Kelvin.