A certain balloon maintains an internal gas pressure of $P_0=100$  $kPa$  until the volume reaches $V_0=20m^3$ . Beyond a volume of $20m^3$ , the internal pressure varies as $P=P_0+2k{\left(V-V_0\right)}^2$  where $P$  is in $kPa,V$  is in $m^3$  and $k$  is a constant $\left(k=1kPa/m^3\right)$ . Initially the balloon contains helium gas at ${20}^{0}C$ , $100kPa$  with a $15m^3$  volume. The balloon is then heated until the volume becomes $25m^3$  and the pressure is 150 kPa. Assume ideal gas behaviour for helium. The work done by the balloon for the entire process in $kJ$  is