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Question

The equation of thermodynamic state of an ideal gas can be expressed as (P+aV2)(Vb)=RT. Here, P is the pressure, V is the volume, T is the absolute temperature and a,b, and R are constants. Which of the following options correctly represents the dimension of a?

A
[ML5T2]
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B
[ML1T2]
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C
[M0L3T0]
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D
[M0L6T0]
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Solution

The correct option is A [ML5T2]
aV2 term has been added to pressure P.
aV2 must have unit of pressure.
[P]=[aV2]
[ML1T2]=[a]([M0L3T0])2
[a]=[ML5T2]

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