the no. of particles is given by n= -d(n2-n1 / x2-x1), find the dimension of d?

Question

The no. of particles is given by n= -d(n2-n1 / x2-x1)crossing a unit area perpendicular to x-axis in unit time where n1 & n2 are no of particles per unit volume, for the value of x meant to x2 & x1, find dimension of d, called as diffusion constant?.......... (Answer=L to the power2 T to the power-1)

Answer 1

You solve this like any other equation.
According to the text you have the following units.

[ ] means dimension

[n] = [L]^(-2) * [T]^(-1)
[n2-n1] = [L]^(-3)
[x2-x1] = [L]

[n] = [d]*[n2-n1]/[x2-x1]

put the above values in:

[L]^(-2) * [T]^(-1) = [d] * [L]^(-3) / [L]

[d] = [L]^(-2) * [T]^(-1) * [L] / [L]^(-3)

[d] = [L]^(-2+1+3) * [T]^(-1)

[d] = [L]^(2) * [T]^(-1)

voila.

Answer 2

Give my colleague Dr. J the ten points.

The question you are asking is about dimensional analysis (DA), which is also called factor analysis, unit analysis, and factor unit analysis. [See source.]

DA is a very powerful tool when working problems of any kind because it is a great way to check your work. For example, we all know F = Ma, but if, just for a moment, we forgot it and wrote down F = M/a and worked our physics problem using this equation how could we catch our mistake? DA.

F = M/a = kg/(m/sec^2) = kg sec^2/m would be the kg-m-sec units on whatever answer we got. We also know our answer should come out in Newtons, whose units are defined as kg m/sec^2.

But the units we got by working F = M/a are not those for Newtons...the acceleration units (m/sec^2) are inverse of what they should be. We made a mistake, we have to inverse the acceleration factor in the bogus equation to make F = M/a into F = Ma.

The lesson here is to always put the units along with the values into your equations. And always use the same metric system for all the terms and factors in the equation. For example, do not use Herz as your unit when 1/sec is the metric unit for a cycle in the kg-m-sec metric system.

Answer 3

huh? Hit enter a couple of times inbetween to make it clearer. Other than that: you already answered the question... didn't you?

Answer 4

since when did they put letters in math?