Intensive Properties of a system- density

[leah3000]

How is density an intensive property?

If density= mass/ volume

wouldn't the density increase as the mass increases seeing that they are directly proportional?

I'm seeing this in my Uni lecture slides on thermodynamics; that density is an intensive property which means it is mass independent but I don't understand that. Is it an error? Or am I thinking of this in the wrong way?

 

[Borek]

wouldn't the density increase as the mass increases seeing that they are directly proportional?

Only if you would be able to keep the volume constant.

 

[leah3000]

Only if you would be able to keep the volume constant.

Ok so i understand that part, but won't the density still fluctuate more or less once the mass or volume is altered?

I guess I'm confused a bit because both mass and volume are extensive properties...so why is density intensive?

 

[Ygggdrasil]

Usually if you take the ratio of two extensive quantities, you will get an intensive quantity. If you double the mass, you also double the volume so the factors of two cancel out when you take the ratio, and density remains the same.

 

[Yanick]

I was taught to imagine the object and then cut it in half and ask yourself if that property has changed. Makes it pretty simple to see how a block of iron, for example, will have the same density as the two blocks you can make by cutting the original in half.

Its not a rigorous mathematical proof, but it helps clear things up when you're unsure.