download the exercise with solution: entropy production gas mixing
Two well-insulated rigid tanks A and B have the same volume (VA=VB=1 m3 ) and both are filled with air with the following thermodynamic states:
Tank A: pA = 1 bar ; TA = 500 K
Tank B: pB = 18 bar ; TB = 500 K
Now these two tanks are connected with each other through a pipe, so that air from tank A and tank B can mix with each other and reach the same pressure in the end. During this mixing process, no heat is transferred.
Determine the entropy production after this mixing process.
Assume that in this case, air is an ideal gas and its specific gas constant is R=287 J/kg∙K
Index 1: state before mixing
Index 2: state after mixing
At first, we calculate the mass of gas in both tanks before mixing:
In order to determine the entropy production, pressure and temperature p2 and T2 after mixing should also be obtained.
The boundary of the control volume chosen in this case encloses both tanks, tank A and tank B. Since both tanks are well-insulated and rigid, there are no heat transfer and work for volume change. Hence we get the simplified equation of the 1st Law of thermodynamics for closed system and the final temperature T2:
→ mA·cv·(T2-TA)+ mB·cv·(T2-TB)=0
→ T2=TA= TB=500K
So the final pressure p2 is:
Then the entropy production is:
We can obtain an important conclusion:
The entropy after gas mixing and expansion will be produced (entropy production >0 ) and therefore this process is irreversible.