# Is 1 liter always equal to 1 cubic decimeter, independently of temperature, pressure, etc?

I recently found this conversion table for the unit conversion $$\rm mmol/m^3 \ \leftrightarrow\ \rm mmol/L$$ (millimoles per cubic meter to millimoles per liter)

My physics is very rusty, but just to be sure, is it true that a liter of liquid always corresponds to a particular volume? (i.e.: Doesn't change with regards to temperature, pressure, etc?)

• This isn't a homework question - OP is asking a (basic but) perfectly reasonable question about unit conversion. – Emilio Pisanty Mar 16 at 16:01
• Google has a unit converting feature which can take input in cubic meters and give you liters. That should suggest the answer ;) – user191954 Mar 16 at 16:01
• @Chair that isn't my question thought is it? I am asking if the conversion always holds (ie: one liter is always a specific amount of volume) regardless of other paramters we change. – DarioP Mar 16 at 16:54
• Meta discussion: physics.meta.stackexchange.com/q/11160/44126 – rob Mar 16 at 17:01
• @DarioP The point I wished to make was that if the unit converter can do such things without specifying other parameters, it strongly suggests that the units measure the same physical quantity. – user191954 Mar 17 at 2:43

Yes, this is correct. The relationship $$1\:\mathrm{L} = 10^{-3} \:\mathrm{m}^3 \tag 1$$ (i.e. one cubic meter is a thousand liters) is universal and it does not depend on anything. The liter is a unit of volume - by definition, it's a cubic decimeter.
To convert between $$\rm mmol/L$$ and $$\rm mmol/m^3$$, simply insert the relationship above: \begin{align} \rm 1\: mmol/L & = \rm 1\:mmol / (10^{-3}\:m^3) \\ & = \rm 10^{3}\:mmol / m^3, \end{align} and vice versa.