- #1

talebone

- 9

- 0

## Homework Statement

An equation of state that has been used to model the behaviour of a fixed amount of a real gas is

(p + a/v

^{2}) (V - b) = ZT

In the equation, Z, a and b are constants, and P represents pressure, V represents volume, and T represents temperature. The constant Z depends on the amount of gas.

Consider what the dimensions of a and b are in terms of the fundamental quantities of mass (M), length (L) and time (T).

Q1

The dimensions of b are

A L

^{3}

B L

^{6 }

C M L

^{-1}T

^{-2}.

D M

^{-1}L T

^{2}.Q2

The dimensions of a are

A L

^{6}.

B M L

^{5}T

^{-2}.

C M L

^{-I}T

^{-2}.

D M L

^{-5}T

^{-1}.

Q3

The value of the constant Z could be expressed in terms of the unit

A W

B W N s

^{-l}.

C N JK

^{-1}.

D J K

^{-1}

## Homework Equations

V = cm^{3}

d = m/v

P = N/m

^{2}

PV = nRT?

W = FD

## The Attempt at a Solution

Ok. I'll be honest these questions are beyond me. At first glance I am tempted to skip it. But then with what little knowledge I had, I gave it a shot.

Q1

For one I know V = L

^{3}. Ok, we'll start there. If I'm finding b, that means L is going to be on top. I can't show it in working, but just looking at the equation, I'm guessing it. So it's either A or B.

Q2

Again it looks like L will be on top. So that leaves A or B.

Q3

Immediately it looks like K will be under. So that leaves C or D. I look at the answer I see Joules which is work (=FD), which has Newtons in it, so I don't think the ans is C. Therefore it must be D.

As you can see, I have no idea how to do these type of questions. I did a google search and found a term 'Dimensional Analysis', and apparently P = M/LT

^{2}. However, this still does not allow me to answer the question. Please if a kind soul can help me out, or is there a website you can direct me which would explain these kind of questions?

Thanks for your time, appreciate it.