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Question

# The equation of state for a gas is given by (P+aV2)(V−b)=RT, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a is

A
[M5LT2]
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B
[ML5T2]
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C
[ML2T2]
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D
[ML5T2]
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Solution

## The correct option is B [ML5T−2]Given equation is (P+aV2)(V−b)=RT From the principle of homogeneity of dimensions, P and aV2 have same dimension. ∴ [a]=[PV2]=[MLT−2L2×(L3)2]=[ML5T−2] Why this question? Tip: Principle of homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same. This principle is helpful because it helps us convert the units from one form to another.

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