Problem Description
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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 oC.
  • 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 (m3).
  • The highest temperature the balloon material can withstand is 50 oC.
  • 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.

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

  • Take the balloon as a control volume. The filling process belongs to unsteady-flow process.
  • Helium can be treated as an ideal gas with R = 2.0769 kJ/kg-K, cP = 5.1926 kJ/kg-K, and cv = 3.1156 kJ/kg-K.