Please answer the following question, and explain step by step. The two tank bel

Question

Please answer the following question, and explain step by step.

The two tank below contain Argon. Argon behaves very closely to that of an ideal gas with constant specific heats (see Figure 4-24 in your text). The valve is opened and a new equilibrium state is reached where the temperature and pressure are uniform throughout. The initial conditions are: Pa = 400 kPa, TA = 100 degree C, = 2 m?, PB = 300 kPa, TB = 50 degree C, = 3 m3. If both tanks and the connecting line are perfectly insulated, determine the final temperature and pressure.

Explanation / Answer

Ideal gas equation

P*V = n*R*T

For A

Pa*Va = na*R*Ta

na = Pa*Va/(R*Ta)

na = 400*1000*2/8.314*373

na = 257.97 moles

Ma = na*MW

Ma = 10.32 kg

For B

Pb*Vb = nb*R*Tb

nb = Pb*Vb/(R*Tb)

nb = 300*1000*3/8.314*323

nb = 335.14 moles

Mb = 13.41 kg

Initial Energy

Ma*Cp*Ta + Mb*Cp*Tb

Final energy

(Ma+Mb)*Cp*T

Energy is same

Ma*Cp*Ta + Mb*Cp*Tb = (Ma+Mb)*Cp*T

Ma*Ta + Mb*Tb = (Ma+Mb)*T

T = Ma*Ta + Mb*Tb/(Ma+Mb)

T = (10.32*373 + 13.41*323)/23.73

T = 344.75 K

T = 71.75 deg

Finally

V = Va + Vb = 5 m^3

P and T are Final pressure and Temperature

n is no of moles

P*V =n*R*T

n = P*V/R*T

Number of moles remains same (since mass can't be destructed)

n = na + nb

P*V/R*T = Pa*Va/(R*Ta) + Pb*Vb/(R*Tb)

P/T = (Pa/Ta)*2/5 + (Pb/Tb)*3/5

P/T = (400/373)*2/5 + (300/323)*3/5

P/T = 0.986

P = 339.92 kPa

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