represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of , will be [2023]

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Solution

Q.
$(P + \frac{a}{V^{2}}) (V - b) = R T$ represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^{2}}{a}$ , will be [2023]

1 bulk modulus

2 modulus of rigidity

3 compressibility

4 energy density

Ans.
(3)

[b] = [V]

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

$∴ [\frac{b^{2}}{a}] = \frac{1}{[P]} = \frac{1}{[B]} = [K]$

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