The equation for real gas is given by , where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of is equivalent to that of : [2025]

Question

The equation for real gas is given by $(P + \frac{a}{V^{2}}) (V - b) = R T$ , where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of $a b^{- 2}$ is equivalent to that of : [2025]

Smart Achievers · Accepted Answer

(4)

Given, $[P + \frac{a}{V^{2}}] (V - b) = R T$

$[P] = [\frac{a}{V^{2}}] \Rightarrow [a] = [P] [V^{2}]$

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

$[b] = [V] = L^{3}$

$[a b^{- 2}] = [M L^{5} T^{- 2} L^{- 6}] = [M L^{- 1} T^{- 2}]$

Dimension of energy density.

Solution

Q.
The equation for real gas is given by $(P + \frac{a}{V^{2}}) (V - b) = R T$ , where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of $a b^{- 2}$ is equivalent to that of : [2025]

1 Planck's constant

2 Compressibility

3 Strain

4 Energy density

Ans.
(4)

Given, $[P + \frac{a}{V^{2}}] (V - b) = R T$

$[P] = [\frac{a}{V^{2}}] \Rightarrow [a] = [P] [V^{2}]$

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

$[b] = [V] = L^{3}$

$[a b^{- 2}] = [M L^{5} T^{- 2} L^{- 6}] = [M L^{- 1} T^{- 2}]$

Dimension of energy density.

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