# Thermodynamics equilibrium problem

1. Apr 11, 2015

### integ8me

Two rigid tanks are connected by a valve. Initially, tank A contains 0.2m3 of n2 at 350k and 100Kpa. tank B contains 0.5m3 O2 at 500k and 250Kpa. The valve between the tanks is open and the two gases are allowed to mix. Assuming constant specific heats at the given temp find the temp of the gases immediately after mixing (474k) and the amount of heat lost if the tanks are allowed to sit and reach equilibrium with the surroundings at 25c (145.8KJ).

I made the assumptions that if the tanks are the control volume initially then Q=0, KE=0, PE=0.
Ma=PV/RT = (100*0.2)/(0.2968*350)=0.19253kg
Mb=PV/RT = (250*0.5)/(.02598*500)=9.62279kg

Mmix = Ma +Mb
Tmix=(Ma/Mmix)*(Ta)+(Mb/Mmix)*(Tb)
I keep getting Tmix=497.061K
I'm supposed to get 474K, am I missing something obvious?

I included boundary work for the second part of the problem and cannot get the correct answer either. Please help if you can

2. Apr 11, 2015

### SteamKing

Staff Emeritus
Re-check your calculation of the amount of oxygen initially present in tank B. You've slipped a decimal point somewhere.

3. Apr 11, 2015

### ehild

The last formula is wrong. Use the moles of the gases, instead of their masses.

4. Apr 11, 2015

### Delta²

Hm the equation for Tmix seems to be derived from Q (lost by oxygen)=Q (absorbed by Nitrogen). Is this the correct way to model this problem? We have gases that are mixing up not that exchange Q through a separation interface...

5. Apr 11, 2015

### Andrew Mason

Since there is no work done on or by the surroundings in this mixing, $Q = \Delta U = n_aC_v\Delta T_a + n_bC_v\Delta T_b$ (on the assumption that they behave as ideal gases). And, since it is adiabatic, Q = 0, so $n_aC_v\Delta T_a = - n_bC_v\Delta T_b$. So it is really just a matter of finding n and initial T for each gas .

AM

6. Apr 11, 2015

### Delta²

what value for R do you use, shouldnt you use R=8,314. All the units are in SI (mind pressure is in KPa so you should multiply x 1000).
There is no work done, use $Q=\Delta U_{O_2}+\Delta U_{N_2}=(n_{O_2}+n_{N_2})C_v\Delta T, T_i=474K, T_f=298K)$

Ok , i see now , you used $R_{specific}$ and calculated masses , however you should use the moles of the gases not their masses as ehild noticed, for both questions.

Last edited: Apr 11, 2015