A certain balloon maintains an internal gas pressure of P_o = 100 kPa until the volume reaches V_o = 20 m³. Beyond a volume of 20 m³, the internal pressure varies as P = P_o + 2k(V-Vo)² where P is in kPa, V is in m³ and k is a constant (k = 1 kPa/m³). Initially the balloon contains helium gas at 20^oC, 100 kPa with a 15 m³ volume. The balloon is then heated until the volume becomes 25 m³ 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 : 

1083

Work done by the balloon :

\(W = \int_{15 m^3}^{20 m^3} P_o dV + \int_{20 m^3}^{25 m^3} pdV\)

  = \(\int_{15 m^3}^{20 m^3} P_o dV + \int_{20 m^3}^{25 m^3} [P_o + 2(V-V_o)^2]dV\)

  = \([100*5 + 100*5 + 2*\frac{(25-20)^3}{3}] kJ = \) 1083 kJ