THERMODYNAMICS  CASE STUDY



Introduction

Problem Graphic


Minnie volunteers to help the new semester welcoming party. Her job is to fill the balloons with helium from a supply line. The balloons have some limitations that she needs to consider when she fills them.
What is known:
 The supply line of helium has a pressure of 120 kPa and a temperature of 25 ^{o}C.
 Mass flow rate from the supply line is 0.01 kg/s.
 The elasticity of the balloon material is such that the pressure inside varies with volume according to the relation P = 10 V, where P is the absolute pressure in the balloon (kPa) and V is the volume of the balloon (m^{3}).
 The highest temperature the balloon material can withstand is 50 ^{o}C.
 A cooling system is used to cool the balloon during the filling process. 6 kJ of heat is taken away by the cooling system per second.






Questions



 Determine how long will it take to fill each balloon?
 Is it safe to use this filling system to fill the balloons?






Approach



 Take the balloon as a control volume. The filling process belongs to unsteadyflow process.
 Helium can be treated as an ideal gas with R = 2.0769 kJ/kgK, c_{P }_{}= 5.1926 kJ/kgK, and c_{v }= 3.1156 kJ/kgK.



