Question

In the equation (𝑃+𝑎/𝑉²)(𝑉−𝑏)=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, determine the units of a and b.

Answer 1

Only the quantities with the same units can be added or subtracted. Thus, from the first term obtain:

$$[P] = \dfrac{[a]^2}{[V]}$$

where $[P] = Pa, [V] = m^3$, and $[a]$ is the units of $a$. Thus, obtain:

$$[a] = \sqrt{[P][V]} = \sqrt{Pa\cdot m^3}$$

Similarly, from the second term obtain:

[V] = [b]\\ [b] = m^3

Answer. Units of $a$ are $\sqrt{Pa\cdot m^3}$, units of $b$ are $m^3$.