The equation of state for a real gas is given by (P + a/V^2)(V - b) = RT. What are the dimensions of the constant a?

A. [ML^5T^-2] — According to the principle of homogeneity, the dimensions of P must be equal to the dimensions of a/V^2. Since P is pressure [ML^-1T^-2] and V^2 is volume squared [L^6], a must have dimensions [ML^-1T^-2] [L^6] = [ML^5T^-2].

JEE Main · PhysicsHard

$The equation of state for a real gas is given by $(P + \frac{a}{V^2})(V - b) = RT$. What are the dimensions of the constant $a$?$

A. $[ML^5T^{-2}]$
B. $[ML^{-1}T^{-2}]$
C. $[M^2L^5T^{-2}]$
D. $[ML^2T^{-2}]$

Show correct answer & step-by-step solution

Correct answer: A — $[ML^5T^{-2}]$

Solution

By the principle of dimensional homogeneity,

[P] = [a / V^{2}]

. Thus,

[a] = [P] [V^{2}] = [M L^{- 1} T^{- 2}] [L^{6}] = [M L^{5} T^{- 2}]

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