What Does Per Unit Volume Mean in Physics?

[GammaMacht]

Hi, often I hear people say that there are "X states per unit volume" or something along these lines. What is meant by unit volume? Is this one cubic meter, a cubic centimeter, or what?

This is a general question about the terminology that people use anytime they say "per unit" something. Thanks for the help!

 

[olgranpappy]

If there are "p" states per unit volume then in a volume of size "V" there are p*V states. See, it works; in a volume of "1 unit" (any unit), a "unit volume" (i.e. a volume of size one) there are p*1 states--p state in a volume of 1.

 

[GammaMacht]

But how is that definition descriptive? For concreteness, let's say that p=5 and so we're saying there are 5 states per unit volume.

You say that there will be p*V states in a volume V. So in a unit volume of 1 m^3, there are supposedly 5 states. But then again, in a unit volume of 1 cm^3 there are also 5 states, although this is inconsistent by 6 orders of magnitude from the previous statement. This is what is confusing me.

Thanks.

 

[cepheid]

That's why you stick to ONE system of units in a given context. In physics we use the SI system, in which the fundamental unit of length is the metre, and therefore the unit of volume is the metre cubed. As a result, it is understood that "per unit volume" means per cubic metre.

To put it another way, the number of states is always p*V. It's just that:

if we're dealing with 1 m^3, then V = 1

if we're dealing with 1 cm^3, then V = $10^{-6}$

 

[angel 42]

To put it another way, the number of states is always p*V. It's just that:

if we're dealing with 1 m^3, then V = 1

if we're dealing with 1 cm^3, then V = $10^{-6}$

Iagree, It depends on your problem, and if your using MKS unit system (meter-Kgram-sec) {{it's also called SI system}} then it'll be the first case that cepheid mentioned , or CGS units (cm-gram-sec) for this you use the second case

 

[GammaMacht]

Okay, so it's simply understood that when saying per unit [units] you mean the standard unit for that system. That answers my question. Yet it seems so much better to simply be explicit and say what units you're talking about. It takes no more time.