Question

The equation of state of a real gas is given by \[ \left( P + \frac{a}{V^2} \right)(V - b) = RT, \] where \( P, V \) and \( T \) are pressure, volume and temperature respectively and \( R \) is the universal gas constant. The dimensions of \[ \frac{a}{b^2} \] is similar to that of :

• A. PV
• B. R
• C. RT
• D. P

Answer 1

The Correct Option is D

In the given equation of state for a real gas:

\(\left( P + \frac{a}{V^2} \right) (V - b) = RT,\)

the term \( \frac{a}{V^2} \) must have the same dimensions as pressure \( P \) since it is being added to \( P \).

The dimensional formula of pressure \( P \) is:

\([P] = [F][A^{-1}] = [M][L^{-1}][T^{-2}],\)

where \( F \) is force and \( A \) is area. Therefore, the dimensions of \( \frac{a}{V^2} \) must also be the same as \( P \).

Since \( \frac{a}{V^2} \) has the same dimensions as pressure

The correct option is (D) : P