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 ^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, c_P = 5.1926 kJ/kg-K, and c_v = 3.1156 kJ/kg-K.