HW #5, P9 - Filling a Balloon with Helium - 10 pts

A balloon initially contains 65 m3 of helium gas at atmospheric conditions of 100 kPa and 22oC. The balloon is connected by a valve to a large reservoir that supplies helium gas at 150 kPa and 25oC. Now, the valve is opened and helium is alowed to enter the balloon until pressure equilibrium with the helium at the supply line is reached. The material of the balloon is such that its volume increases linearly with pressure. If no heat transfer takes place during this process, determine the final temperature of the helium in the balloon.

This is a transient or unsteady process because helium enters the system (the balloon). Assume the He behaves as an ideal gas, but check to see if this is a good assumption. Use the IG EOS to determine the initial mass of He in the balloon. After you determine V2, calculating Wb is easy ! Then, simultaneously solve two equations in two unknowns. The equations are: the IG EOS applied to the final state of the balloon and the transient form of the 1st Law applied to this process. The two unknowns are: T2, mHe,2 .
The catch is that we must determine values for U1, U2 and Hin. These are NOT ΔU's and ΔH's but real U's and H's. In order to do this (just like the steam tables) we MUST choose a reference state. A reference state is a T, P and phase at which YOU choose to make EITHER U or H zero kJ/kg. I want you to use a reference state of U = 0 for He gas at 22 oC and 100 kPa. The P doesn't actually matter because He is treated as an IG in this problem so U and H are not functions of P anyway.

Once you have a ref state, use a Hypothetical Process Path from the ref state to states 1, 2 and inlet to evaluate U1, U2 and Hin using the IG EOS and CV and CP given in the problem.

For He, use: CP = 5.1926 kJ/kg-K and CV = 3.1156 kJ/kg-K.