The equation of state of a real gas is given by (P+a/V²)(V-b)=RT, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of a/b² is similar to that of :

Solution

Physics sir · 3 steps

Only like quantities add, so a/V² is a pressure and b is a volume. Then a/b² is just a/V² again.

1. Match terms to P. You can only add quantities with the same dimensions. So a/V² must have the dimensions of pressure, which gives [a] = [P][V²].
2. Match b to V. In the same way, b is subtracted from V, so b has the dimensions of volume: [b] = [V] and [b²] = [V²].

   [a/b²] = [P][V²]/[V²] = [P] = [M L⁻¹ T⁻²]

3. So. a/b² has the same dimensions as pressure P, which is option (a).

The idea to keep. In any physical equation, each term in a sum or difference has the same dimensions as the others. Use that to read off the dimensions of unknown constants, one bracket at a time.

Answer from the NTA final answer key. Solution by PrepWiser.