A certain elastic balloon will support an internal pressure equal to Po 100 kPa until the balloon becomes spherical at a diameter of Do 1 m, beyond which P = Po + C(1-x6)x ; x = Do/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.
Balloon becomes spherical at V0 = (/6) x (1)3 = 0.5236 m3 and the initial mass is
m =P1V1/RT1 = 100 x 0.4/2.07703 x 250 = 0.077 kg