Question

if (p+a/v2) (V-b)= RT find the dimension of a/b

Answer 1

Problem:

If $\left(p + \frac{a}{V^2}\right)(V - b) = RT$ find the dimension of $a/b$.

Solution:

The given equation is the Van der Waals equation of the state of gas, where $p = [Pa]$ – pressure of gas

$$V = [m^3] \text{ – volume}$$ $$R = \left[\frac{J}{mol*K}\right] \text{ – universal gas constant}$$ $$T = [K] \text{ – temperature}$$

a, b – some constants

As in the equation pressure is added to $\frac{a}{V^2}$, this two physical quantities have the same dimensions. The same way we consider $V$ and $b$ have the same dimensions too. Thus, the dimension of $a$ is the same as the dimension of $p * V^2 = [Pa * m^6]$, and dimension of $b$ is $b = [m^3]$. Then

$$\frac{a}{b} = \left[\frac{Pa * m^6}{m^3}\right] = [Pa * m^3]$$

where

Pa – pascal

m – meter