The equation of a real gas is (P + a/V²)(V - b) = RT, where P, V, T and R have their usual meanings. The dimension of ab⁻² is equivalent to that of:
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Question

The equation of a real gas is (P + a/V²)(V - b) = RT, where P, V, T and R have their usual meanings. The dimension of ab⁻² is equivalent to that of:

G1 Physics · Accepted Answer

From the equation, the term a/V² must have the dimension of pressure. [P] = M L⁻¹ T⁻², [V] = L³. Therefore [a] = [P][V]² = (M L⁻¹ T⁻²)(L⁶) = M L⁵ T⁻². Also, b has the dimension of volume: [b] = L³. Hence [ab⁻²] = (M L⁵ T⁻²)(L³)⁻² = M L⁻¹ T⁻². Energy density has dimension [Energy/Volume] = (M L² T⁻²)/L³ = M L⁻¹ T⁻². Therefore ab⁻² has the dimension of energy density. Correct option: D.