# Why "a liter of water" but not "a 100ºC of water"?

Imagine a volume of water, 100 ml in size, with a temperature of 100ºC. Interestingly, you can refer to the water as "100ml of water" but you cannot call it "100ºC of water". That is one interesting difference between those two properties, size and temperature.

There is another well-known difference between size and temperature: size is an extensive quantity. In other words, it is additive: the size of an object is the sum of the sizes of its parts. Temperature is an non-extensive a.k.a. intensive quantity. That is, the temperature of an object is not the sum of the temperatures of its parts. Combining two 100ºC liters of water does not yield a two-liter volume of water at 200ºC.

Is there a rule that you can refer to an object using phrases like "this [quantity]" and "a [quantity]" only if the quantity is extensive? Some other cases seem to fit this rule:

• If a block of wood has a mass of one kilogram, you can call it "a kilogram of wood". Mass is an extensive quantity, since the mass of an object is the sum of the masses of its parts.
• Similarly, if the block of wood has a mass of 100g, you can call it "100g of wood."
• If a piece of music lasts one hour you can call it "an hour of music". Duration is an extensive quantity, since the duration of an object is the sum of the durations of its temporal parts, i.e. the stages of its lifespan.
• Similarly, if the piece of music lasts 100 seconds, you can call it "100 seconds of music."
• However, if a train is moving at 100 mph, you cannot call it "100 mph of train". Speed is an intensive magnitude, since it is not additive: the speed of the train is not the sum of the speeds of its cars.
• If a song is 100 decibels, you cannot call it "100 decibels of music". Decibel level is an intensive quantity, since it is not additive. The decibel level of an album is not the sum of the decibel levels of all of its tracks.

Have linguists discussed this rule anywhere?

• Isn't it simply that the "of" construction expresses the amount of something, but temperature, speed etc are not about amount?
– TKR
Oct 24, 2021 at 22:00
• That might be it. Extensive quantities are plausible answers to the question, "How much of it is there?" (One kilo, one liter, one hour, etc.) So, those terms don't just measure the size, mass, and duration of the thing; they measure the thing itself. Not so with intensive quantities. But then, I'm curious why this is. Why do we tend to identify a thing with its duration, mass, or volume, but not its intensities? Oct 25, 2021 at 1:51
• Why not? Zero grams of wood means there is no wood. A train moving at 0 mph is still a train that exists. Oct 25, 2021 at 4:20
• I’m not convinced that ‘100 decibels of music’ isn’t possible. It’s certainly not the standard way to refer to the loudness of music, but it seems possible to me in a context like, “Our ears were suddenly bombarded with 110 dB of hardcore rock music, and I nearly fainted”. Also note that, while ‘100° of water’ is nonsensical, ‘five degrees of separation’ is perfectly normal. May 29 at 7:21

I believe what you are seeing is the difference between Partitive and a normal DP.

Partitive indicates that the phrase is about a quantified subset of a bigger set of objects.

Some languages even have a separate noun case for that. Most notably, Finnish:

pala juustoa = a piece of cheese

Some Slavonic languages, including my native Ukrainian, use Genitive case for this function.

On the contrary, if you refer "a 100 decibel sound", this is a normal Determiner Phrase; you chose a single object among of others that are playing at different loudness. Some languages that expose agglutinative features are able to build complex adjectives for that purpose, e.g. `hundred+decibel+ADJ`.

Compare these two phrases:

Give me half a kilo of cabbage (1)
Give me a half-kilo cabbage (2)

(1) would be the Partitive because you refer a part of a common;
(2) would be a normal DP because you are choosing a single one by a certain characteristic.

• Just a note: "a 100 decibel music" is ungrammatical in English, since "music" is uncountable. Oct 25, 2021 at 8:04
• "A 100-decibel sound" on the other hand is perfectly fine for me (since countable).
– Draconis
Oct 25, 2021 at 15:27
• I think DPs like a pound of cheese are usually known as pseudo-partitives or the genitive of measure, “ While the true-partitive relation implies proportional quantification, pseudo-partitives denote plain quantification such as amounts (a group of people), measures (a cup of tea) or quantities (a lot of people, a majority of people) of particular kinds (people, tea).[19] Therefore, pseudo-partitives are sometimes referred to as quantitative partitives (e.g., Ihsane 2013). May 29 at 13:04
• (cont.) Accordingly, pseudo-partitives do not encode a relation between two referents but rather encode just one referent that is quantified or measured” Seržant 2021 Typology of partitives Barbara Partee has written extensively on this topic. May 29 at 13:04