Question

Two rigid tanks are connected by a valve. Initially, one tank contains 10 mº of helium (He) gas at 220 kPa, 40°C? The other tank initially contains 4.0 R of neon (Ne) gas at 150 kPa, sot. Now the valve is opened, allowing the two gases to mix with each other. Heat transfer occurs during the mixing process. The final equilibrium temperature is 44'C. The specific heats of monatomic gases are independent of temperature. Determine: (a) the final volume of the mixture, (b) the molar fraction of each gas after mixing, (c) the final pressure of the mixture, (d) the amount of heat transfer during this process, (e) the amount of entropy change during this process.

Answer 1

Gas Constant:

(i) For Neon - R = 0.4119 Kj/kg.k

(ii) For helium - R = 2.0769 Kj/kg.k

The detailed solution is given below:

mone = Akg GivenVhe = lom m = 44 °C Pue = 2zontal Pire 150kpa The = 400 The = 500 Kang)x (0.4119 KT1kg.K) XCSo+273W) (Soupa) (volume of neon) Vine MRT Р Ne = 3.55m3 Now, V final V total Vhet Vive = 10 +3.55 - 13.55m3 6 → Mass of helium gas, mue "He = V XP RT The 10 ) x 220) (2.0369 ) (4/2536) 3.38kg # The number of moles : - Nue Mie Mue 3.38 kg 0.845 kmol 4 kg Ikmal → None = Moe Ак. = 0.1982 kmol More 20.183 kg/kmol

Now, total number of moles, Non = Nie + Nwe = 1.0432 kmol # The mole fraction : → Yne = Nine- Nm 0.1900 The Nhe 0.81001 Nm CS # The final pressure Pm = TN Rut (1.0432)(8.314)x(44+243*) (13.55) 202.91kba Ne = Q- WŁAE = = 0.6179 kilig.k and Cryte = 3.1156 KJ 156 15 ingok The energy balances o+A0 [w-o] → Q = Aung + AUME = (ma+Une + (Umuime [mer (Tm-1)] Ne + [mer + / mer (Tm-T) $ 14:40 F) (423)*(3*)] }+{30(3152)(atna) The

- (101273)]} => Q = -14.8296+ 42.1229 = 27.29 kJ to the i. Min = 27.2945 (positive sign indicate heat toansfer the system) ke) The entropy change, S2-S, = m (se-s, Im - ne tom feasi ) he] # The Nowy [mcsa.-5. We m[Coln Im _ R ln Y Pm Ne = {141 601920 Vn_317. - (0.4119) In [202.91 0,19 323 150 = 2.16 119 kJlK and T PI He [mce sve = { mCarang { [Cape Togo den for - fawy[simus longs - Provo) In 317 – (2.0769) In 202.91X0.81 313 220

. 2. 36 480 кг/k PS-S, А. 431 1 кота