# Homework Help: Principle of corresponding states

1. Mar 19, 2015

### decerto

1. The problem statement, all variables and given/known data
Show that it is always possible to adjust measurement units such that a; b can be assigned any values
you want. This means that e.g. all van der Waals gases look exactly the same if the units are
accordingly adjusted. (This is what is called principle of corresponding states).

2. Relevant equations
$P=\frac{T}{v-b}-\frac{a}{v^2}$

3. The attempt at a solution

So the question before this one was to work out the critical values for P, v and T for the van der waals equation of state + 3 other qualitatively similar gas models, the critical values were all of the form $P_c \propto \frac{a}{b^2}$, $T_c \propto \frac{a}{b}$ and $v_c \propto b$ but Im not sure if this is relevant.

The question is confusing me to be honest, shouldnt it be trivially true that you can change your definition of a metre or kilogram in different cases to get the same values for different gasses?

Last edited by a moderator: Mar 19, 2015
2. Mar 19, 2015

### Staff: Mentor

This is most certainly very relevant (hint!).

For any pair of coefficients a and b? No, you can't do that by units alone. But you can do it using another rescaling, see my hint above.

3. Mar 19, 2015

### Staff: Mentor

I agree that the problem statement isn't too clear. But, I would start out by writing:

$P_r=P/P_c$

$v_r=v/v_c$

$T_r=T/T_c$

These are the reduced pressure, the reduced volume, and the reduced temperature of the gas, respectively, and all three are dimensionless. I would then substitute for P, v, and T in the vdw equation and lump all the extra critical properties in with the a and b.

Chet

Ooops. I just saw Dr. Claude's post which basically suggests the same thing (a little more subtily).

4. Mar 19, 2015

### decerto

The question after this is about finding the reduced form of the equation which I have already done. This question seems to be about justifying it. I think Dr Claude is suggesting something different

5. Mar 19, 2015

### decerto

The following question asks me to put the equations in reduced form where $P_c$, $T_c$ and $v_c$ are equal to 1 if that is what your suggesting I do for this question as chestermiller says.

If not then does the fact you can write p, T and v in such a way as to be independent of a and b mean anything