A certain elastic balloon will support an internal pressure equal to P_o = 100 kPa until the balloon becomes spherical at a diameter of = 1 m, beyond which 

P = P_o +C(1-x⁶)x ;

 x = D_o/D 

because of the offsetting effects of balloon curvature and elasticity. This balloon contains helium gas at 250 K, 100 kPa, with a 0.4 m³ volume. The balloon is heated until the volume reaches 2 m³. During the process, the maximum pressure inside the balloon is 200 kPa. 

(a) What is the temperature inside the balloon when pressure is maximum? 

(b) What are the final pressure and temperature inside the balloon?

(c) Determine the work and heat transfer for the overall process. (R=2.0770kJ/kgK, c_v=3.1156kJ/kgK). [1731.25K, 196.15kPa &2452K, 289.77kJ & 818kJ]