Question

ANSWERS provided are just "ballpark values"... DO NOT WORK BACKWARD FROM THESE ANSWERS. NINE kg of AIR and FOUR kg of HELIUM GAS are sealed in a rigid and insulated intenal-piston-cylinder device. Initially the helium is at 300 K and 800 kPa. The air is at 900 K and 200 kPa. When released, the rigid piston moves slowly and conducts heat from the hot gas to the cold gas. The mass and energy of the piston material are negligible. But internal friction is not negligible. This is not a quasi-equilbrium process. Use the gas data given below. Find all initial state and final equilibrium state properties. Tabulate initial and final (p,T,v,m,V, E) for the AIR & HELIUM. Air: k 7/5, R 0.2870 kJ/kg-K With Cv= R/(k-1) = 0.7175 kJ/kg-K Air m 9 kg T, 800 K p1 200 kPa Helium m =4 kg Ti 300 K pi 800 kPa Helium: k 5/3, R= 2.0773 kJ/kg With Cv = R/(k-1) = 3.1160 kJ/kg-K ans) T2-500 K FIND the pressure and temperature when the gases reach equilibrium. Prinal kPa and Tinal. _K

Answer 1

Given Air ma 9 kg, Ta - 900 k , Pa= 2oo KPa Air He R o 287 Helum mh 4 Kg , Th= 300k , Ph 800 kPa R 2.0773 kSIkgk Cu 3Go \eT/leg k Here Systcm is insulated hence here is No heat tans fer CQo) also when piston move the usork does not CYOSS benie considered the boundary of system to worle is be zero (u-o) According 1t lais of themodynamics du o duit duz- o Here TFS Anal Temp Ma Cva T Ta') mn Cun ( Te- Th) -O 9x o.7175 x( TF - q00) 4x 3.116 x ( Te - 3od)- D Soluing above eq, we geh Te 504.767 K Ary Noca Ideal qas lao PV=mRT PV mT we know here du = o Iniha

Suffix m mixture (final state maua mp Un MmUm since ud T MaTa mTh mm Tm ui ba us ba Pp Final Pressure Pa Va Ph Vh P Vm Ra Rn Rm Now Pa Va = ma R Ta . Va ma Ra Ta gx o.287 x 900 -. 62 m3 Pa 200 similay 4x 2 0773 x 300 Vn mh Rh Th 3.116 m3 We knou tha Vm VatVn 4.736 m3 Vm .62 +3.116 - Now maRa t mh Rn mm Rm I xo 287 + ux 2.0773 maRa t mn Rn Rm = (mat mn) KJ/cgk uSing ea & Rm Pf x IL.73 (g+4) x 504.767 o 837 PF 372.71 KPa Anu