(P + a/V²)(V − b) = RT represents an equation of state. P is pressure, V is volume, T is temperature and a, b, R are constants. The physical quantity having the same dimensional formula as b²/a is:
Physics · Circular Motion
JEE Mains 1 February 2023 Shift 1 Morning Shift

Question

(P + a/V²)(V − b) = RT represents an equation of state. P is pressure, V is volume, T is temperature and a, b, R are constants. The physical quantity having the same dimensional formula as b²/a is:

Physics · Circular Motion

G1 Physics · Accepted Answer

Since a/V² has dimensions of pressure, [a] = [P][V]². Also [b]=[V]. Therefore [b²/a]=[V]²/([P][V]²)=1/[P], which is the dimension of compressibility.