The equation for real gas is given by (P+a/V²)(V-b)=RT, where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of ab⁻² is equivalent to that of :

Solution

Physics sir · 3 steps

Each term in a bracket must have the same dimension, so a/V² is a pressure and b is a volume.

1. Find a. You can only add like quantities, so a/V² has the dimension of pressure. That gives [a] = [P][V²].
2. Find b. In (V - b), b is subtracted from a volume, so [b] = [V] and [b²] = [V²].

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

   Option	Dimension	Matches [ML⁻¹T⁻²]?
   Compressibility, 1/P	[M⁻¹ L T²]	No
   Planck's constant, E/ν	[M L² T⁻¹]	No
   Energy density, E/V	[ML²T⁻²]/[L³] = [ML⁻¹T⁻²]	Yes
   Strain, (Δ L)/L	dimensionless	No

3. So. ab⁻² has the dimension of pressure, which is the same as energy per unit volume. The answer is (c), energy density.

The idea to keep. Terms you add or subtract must share a dimension. Also remember: pressure, stress, Young's modulus and energy density all have the dimension [ML⁻¹T⁻²].

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