Question

Find the dimensions of constant a and b occurig in van der Waal's equation . [p+a/v2][v-b]=RT

Answer 1

(P + a/V^2) (V - b) = RT
P is pressure, V is volume and T is temperature.
[P] = [F/A] = [MLT^−2/L^2] = [ML^−1T^−2]
[V] = [L^3]

We cannot add or subtract quantities of different dimensions. Therefore
[P] = [a/V^2] ⇒ [a] = [PV^2] = [ML^−1T^−2 L6] = [M L^5 T^−2]
∴ [a] = [M L^5 T^−2]

Similarly,
[b] = [V] = [L^3]

Answer 2

Answer:

Concept:

Van der wall's equation.

Explanation:

$\left(p+a / V^{2}\right)(v-b)=R T$

As pressure can be added only to pressure, therefore, a/V2 represents pressure, p

$i.e. \quad \frac{a}{\mathrm{~V}^{2}}=\mathrm{P} \\or, \quad a=p \mathrm{~V}^{2}$

$\left.=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] \mathrm{L}^{3}\right]^{2} =\left[\mathrm{M}^{1} \mathrm{~T}^{5} \mathrm{~T}^{-2}\right]$

Again from the 'v' that is volume, we can represent 'b' as below by subtracting only volume 'v'

$\text { or } b=V=\left[\mathrm{L}^{3}\right]=\left[\mathrm{M}^{0} \mathrm{~L}^{3} \mathrm{~T}^{0}\right]$

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