The pressure $p$, volume $V$ and temperature $T$ for a certain gas are related by $p=\frac{A T-B T^{2}}{V}$ where $A$ and $B$ are constants. The work done by the gas when the temperature changes from $T_{1}$ to $T_{2}$ while the pressure remains constant, is given by

• A
  $A\left(T_{2}-T_{1}\right)+B\left(T_{2}^{2}-T_{1}^{2}\right)$
• B
  $\frac{A\left(T_{2}-T_{1}\right)}{V_{2}-V_{1}}-\frac{B\left(T_{2}^{2}-T_{1}^{2}\right)}{V_{2}-V_{1}}$
• C
  $A\left(T_{2}-T_{1}\right)-\frac{B}{2}\left(T_{2}^{2}-T_{1}^{2}\right)$
• D
  $\frac{A\left(T_{2}-T_{1}^{2}\right)}{V_{2}-V_{1}}$