dr At steady-state, what is the numerical value of the state variable deseribing

Question

dr At steady-state, what is the numerical value of the state variable deseribing the system mass? (b) Consider the air-filled tank shown in the Figure 2 below. The dynamic mass balance around the atr-flled, 10.0 L. rigid pressurized tank at sea- level is described by the following equation: dr where, m is the mass of air in the tank and Gas behavior can be deseribed by ideal gas law. The system and aubient temperature is 298 K. Initially, the gauge pressure records the air in the tank to be 2500 kPa. The valve is opened at some point in time. What is the aumerical value of system mass at steady Pande is the gauge pressure of air in the tank.

Explanation / Answer

dm/dt = - aPinside

Here, Pinside = Pgauge = P - Patm , where P is the absolute pressure in the tank.

Now, by ideal gas law,

moles n = Pv/RT

mass m = PMv/RT, where M is the molar mass.

In SI units, M = 0.0288 kg, v= 0.01 m3 R = 8.314 J/mol-K T = 298 K

Thus, m = 1.162428 x 10-7 P   ( P in Pascal)

Also, Patm = 101325

Thus, we have

1.16428 x 10-7 dP/dt = P - 101325

At steady state, dP/dt = 0 giving P = 101325 Pa

Plugging in the equation for mass,

m = 1.162428 x 10-7 x 101325 kg = 0.01178 kg -- Mass at steady state

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