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The equation of state of \( n \) moles of a non-ideal gas can be approximated by the equation \( \left(P+\frac{n^{2} a}{V^{2}}\right)(V-n b)=n R T \),
\( \mathrm{P} \) where \( a \) and \( b \) are constants characteristic of the gas. Which of the following can represent the equation of a quasi-static adiabatic for this gas (assume that \( C_{V} \), the molar heat capacity at constant volume. Is independent of temperature)
[KVPY 2013]
(a) \( T(V-n b)^{R / c_{V}}= \) constant
(b) \( T(V-n b)^{C_{V} / R}= \) constant
(c) \( \left(T+\frac{a b}{V^{2} R}\right)(V-n b)^{R / c_{V}}= \) constant
(d) \( \left(T+\frac{n^{2} a b}{V^{2} R}\right)(V-n b)^{c_{V} / R}= \) constant
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