Van der waals,equation of state is(p+a/v²)(V-b)=nRT. The dimensions of a and b

Van der waals,equation of state is(p+a/v²)(V-b)=nRT. The dimensions of a and b are

(a) [ML³T²],[ML³T⁰]
(b) [ML⁵T⁻²],[M⁰L³T⁰]
(c) [M²LT²],[ML³T²]
(d) [ML²T],[ML²T²]

[ML⁵T⁻²],[M⁰L³T⁰]

((p+a/v²)(V-b)) / nT =R

Since we have $(p - \frac{a}{V^{2}})$ , the term $(p - \frac{a}{V^{2}})$ needs to have units of pressure for subtraction to proceed.

Therefore, a V ² = pressure

a = pressure x

∴ \frac{a}{V^{2}} \equiv pressure ⟹ a \equiv pressure \cdot (volume)^{2}

=[ML⁻¹T⁻²] x (L³)

∴ \frac{a}{V^{2}} \equiv pressure ⟹ a \equiv pressure \cdot (volume)^{2}

=ML ⁵T⁻²

In case of variable b, it should be same as volume as v-b should work.

b=(L³)

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