The equation of state of $n$ moles of a non-ideal gas can be approximated by the equation $$ \left(P+\frac{n^{2} a}{V^{2}}\right)(V-n b)=n R T $$ where a and b are constants characteristic of the gas. Which of the following can represent the equation of a quasistatic adiabat for this gas (Assume that $\mathrm{C}_{\mathrm{V}}$, the molar heat capacity at constant volume, is independent of temperature)?

• Correct answer
  A

  $T(V-n b)^{R / C_{v}}=$ constant
• B

  $\mathrm{T}(\mathrm{V}-\mathrm{nb})^{\mathrm{C}_{\mathrm{v}} / \mathrm{R}}=$ 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

Hence, the correct answer is option: 'A'.