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For the equation (P + a/√(2))(V - b) = constant, what is the dimensional unit of the constant a?

1. dyne cm⁵
2. dyne cm⁴
3. dyne/cm³
4. dyne cm²

Correct answer: dyne cm⁴

Solution

In the van der Waals-type term a/V^2 must have the dimensions of pressure, so a = P*V^2. In CGS, P is dyne/cm^2 and V^2 is cm^6, giving a = (dyne/cm^2)*cm^6 = dyne*cm^4.

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