Dimensions of physical quantities

[Anique]

Hello there,
I have a confusion between dimensions and units! All of others tell me its not unit but some use units! Please verify the following

Quantity Dimension
Length L
Mass M
Time T
Temperature Θ
Amount of subst N
Luminous intensity J
Current I

Is it right? Also please let me know if the dimension of IDEAL GAS CONSTANT is:
R = ML²T^-2N^-1Θ^-1

Thank you

 

[Bandersnatch]

Hi Anique,

What exactly is the confusion? A dimensions is what you measure, for example length, mass. A unit is what you measure the dimension in. E.g. units of length are metres, feet, light-years etc.
In dimensional analysis you always want the most fundamental dimensions possible, so rather than calling force a dimension, you express it in terms of more fundamental dimensions: MLT^-2 (since Newton is kg*m/s^2)

Also please let me know if the dimension of IDEAL GAS CONSTANT is:

It's correct.

 

[Anique]

Dear Bandersnatch,

Thank you very much! I saw on some places people using mol as a DIMENSION for amount and K as a DIMENSION for Temperature. That made me confused!

Thanks for your support! :)

 

[Anique]

What exactly is the confusion? A dimensions is what you measure, for example length, mass. A unit is what you measure the dimension in. E.g. units of length are metres, feet, light-years etc.
In dimensional analysis you always want the most fundamental dimensions possible, so rather than calling force a dimension, you express it in terms of more fundamental dimensions: MLT^-2 (since Newton is kg*m/s^2)

Dear Bandersnatch,

Thank you very much! I saw on some places people using mol as a DIMENSION for amount and K as a DIMENSION for Temperature. That made me confused!

Thanks for your support! :)

 

[Bandersnatch]

I saw on some places people using mol as a DIMENSION for amount and K as a DIMENSION for Temperature. That made me confused!

Right, you can see it used that way sometimes.
You can also see for example "length" being called "units" of position (x). Or dimension being called quantity. The important bit is to keep it consistent across the board, so that you don't mix something like "length" and "kilograms", or "mass" and "Kelvins" in your analysis.

Sticking to unitless dimensions should be prioritised, though, as it let's you analyse whatever equation you're analysing without bothering with what particular system of units you ought to use (i.e., metric, cgs, imperial etc.).

Anyway, this is a nice tutorial on dimensional analysis:
http://vallance.chem.ox.ac.uk/pdfs/UnitsAndDimensions.pdf
Give it a read if you get confused again.

 

[Anique]

Dear Bandersnatch,

Anyway, this is a nice tutorial on dimensional analysis:
http://vallance.chem.ox.ac.uk/pdfs/UnitsAndDimensions.pdf
Give it a read if you get confused again.

You help rendered me great support! Especially the "Green Book" is really informative!
Many many thanks! And Hope you will help me again whenever I get stuck somewhere! :-)