a) Determine the mass of the argon after the membrane ruptures (mrota). b) Determine the temperature T, and pressure P, of the argon at state 1. c) Determine the temperature T2 and volume V2 of the argon at state 2. d) Determine the temperature T3, the pressure P, and volume V, of the argon at state 3. e) Determine the total specific work from state 1 to state 3 (;w3). f) Determine the heat transfer that takes place from state 1 to state 3 (;Qs).
a) Determine the mass of the argon after the membrane ruptures (mrota). b) Determine the temperature T, and pressure P, of the argon at state 1. c) Determine the temperature T2 and volume V2 of the argon at state 2. d) Determine the temperature T3, the pressure P, and volume V, of the argon at state 3. e) Determine the total specific work from state 1 to state 3 (;w3). f) Determine the heat transfer that takes place from state 1 to state 3 (;Qs).
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Transcribed Image Text:Membrane
Servo-controlled Arm
А
В
Patm
Piston
Transcribed Image Text:A frictionless piston cylinder system containing argon (Ar) is initially divided by a rigid membrane into two
sections as shown in the figure below. The membrane is a perfect insulator and there is no heat transfer
between the sections. Initially section A has a volume of VA = 13 L and the total combined volume (section
A and section B) is Vrotal = 20 L. The diameter of the piston is 60 cm. The initial pressure of section B is 1000
kPa. The initial temperature of section A and section B is 100°C and 250 °C, respectively.
The membrane ruptures and the argon in section A and B comes to a uniform state (state 1) with a volume
(V:) of 22 L. A servo-controlled arm then extends, coming in contact with the piston but exerting no force
during state 1. While the piston is in contact with the arm, the servo-controller controls the
expansion/compression of the piston. The servo-controlled arm keeps constant contact with the piston
throughout the process. During the first process (state 1 to state 2), the volume is decreased
polytropically, with a polytropic exponent of n = 1.4, to a pressure (P2) of 160 kPa. In the second process
(state 2 to state 3), the volume is then expanded simulating a spring compressing with a spring constant
k, = 100 kN/m and continues until the volume (V3) is double the volume of state 2. Treat argon as an ideal
gas. Patm = 101.3 kPa.
a) Determine the mass of the argon after the membrane ruptures (mīotal).
b) Determine the temperature T1 and pressure P, of the argon at state 1.
c) Determine the temperature T2 and volume V2 of the argon at state 2.
d) Determine the temperature T3, the pressure P; and volume V3 of the argon at state 3.
e) Determine the total specific work from state 1 to state 3 (1w3). {
f) Determine the heat transfer that takes place from state 1 to state 3 (,Qs).
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