A 0.2 m3 tank containing helium at bar and 22 C will be used to supply 4.5 moles

Question

A 0.2 m3 tank containing helium at bar and 22 C will be used to supply 4.5 moles per minute of helium at atmospheric pressure using a controlled adiabatic throttling valve. (a) If the tank is well insulated, what will be the pressure in the tank and the temperature of the gas stream leaving the throttling valve at any later time t? (b) If the tank is isothermal, what will be the pressure in the tank and the pressure in the tank as a function of time? Assuming helium to be an ideal gas with a constant heat capacity of 22J/(mol K), and that there is no heat transfer between the tank and the gas.

Explanation / Answer

I think it's most illustrative to start with the entropy balance:

No Q? since it's adiabatic, and no S?gen since I guess we're assuming it's reversible. One output stream with N?=?4.5 mol/min gives

Solving this gives

For a closed system, my book derives relationships between entropy changes and two of volume, pressure, or temperature changes via the 1st law:

From here it integrates this to arrive at something like

However, this is for constant N! With the helium tank, it is an open system and N is not constant! So I don't see how I can proceed further. Without an entropy balance, the mass and energy balances alone are not enough to solve the system.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.