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(P + a/(V²))(V - b) = RT represents the equation of state of some gases, where P is the pressure, V is the volume, T is the temperature and a, b, R are constants. The physical quantity which has the same dimensional formula as (b²)/a will be

Asked in JEE Main 1st Feb 1st Shift 2023 · Gas laws and P-V-T processes

Answer: (2) Compressibility

Step-by-step solution

Every term added to P must itself be a pressure, so [a/(V²)]=[P], giving [a]=[P][V²].

Every term subtracted from V must be a volume, so [b]=[V].

[(b²)/a]=([V]²)/([P][V]²)=1/([P]).

A reciprocal pressure is compressibility, the reciprocal of bulk modulus.

Why the other options are wrong

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