A tank with an internal volume of 1. m3 contains air at

Chapter 5, Problem 177P

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A tank with an internal volume of \(1 \mathrm{~m}^{3}\) contains air at \(800 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\). A valve on the tank is opened allowing air to escape and the pressure inside quickly drops to \(150 \mathrm{kPa}\), at which point the valve is closed. Assume there is negligible heat transfer from the tank to the air left in the tank.

(a) Using the approximation \(h_{e} \approx\) constant \(=h_{e, \text { avg }}=\) \(0.5\left(h_{1}+h_{2}\right)\), calculate the mass withdrawn during the process.

(b) Consider the same process but broken into two parts. That is, consider an intermediate state at \(P_{2}=400 \mathrm{kPa}\), calculate the mass removed during the process from \(P_{1}=800 \mathrm{kPa}\) to \(P_{2}\) and then the mass removed during the process from \(P_{2}\) to \(P_{3}=150 \mathrm{kPa}\), using the type of approximation used in part (a), and add the two to get the total mass removed.

(c) Calculate the mass removed if the variation of \(h_{e}\) is accounted for.

Equation Transcription:

Text Transcription:

1 m^3

800 kPa

25C

150kPa

h_e anstant =h_e=mg= 0.5(h_1+h_2)

P_2=400kPa

P_1=800kPa

P_2

P_3=150kPa

h_e