A closed frictionless pistoncylinder device containing 65 kg

A closed, frictionless piston-cylinder device containing 65 kg of Nitrogen (N) undergoes a process mixture at a pressure of 1084.6 kPa. The mass of saturated vapor in the system a useful tabie values at back of exam 1. Find the total volume of the system at State 1. (2 points h several equilibrium states. At State 1, the device contains a saturated t State 1 is 20 kg NOTE 50.0152 Pa for State 2 2. Now the system undergoes isothermal expansion until it reaches equilibrium at 500 k What was the change in system volume during this expansion? (2 points) Pv RT AV PRT gas canstaet (.002 4 = o.OL2318 500 Kfa 0.0023 06

Solution

1.)

Given mass of N₂ = 65 Kg

mass of saturated vapour = 20 kg

quality of steam = M_g / ( M_f + M_g ) = 20 /65

x = 0.3

From steam tables saturated at P = 1084.6 KPa

T =105

v_f = 0.001522

v_g = 0.0221

h_v = -61.24

h_g = 87.35

V = v_f + x ( V_g -V_f )

v = 0.001522 + 0.3 ( 0.0221 - 0.001522 )

v = 0.0076954

Volume V = M v = 65 * 0.0076954

V = 0.5 m³

2.)

Now the gas expands isothermally to pressure 500 KPa

at p = 500 Kpa and T = 105 C

interpolating table for T= 105

105 = 100 + x ( 120 - 100 )

x= 0.25

v2 = 0.05303 + 0.25 (0.06701 - 0.05303 )

v₂ = 0.056525

h₂ = 94.46 + 0.25 (118.12 - 94.46 )

h₂ = 100.375   

Volume V= Mv₂ = 65 * 0.056525

V₂ = 3.674 m³

Change in system volume = V₂ - V₁ = 3.674 - 0.5

Change in system volume = 3.174

3.)

For p= 1084.6

h_v = -61.24

h_{a =} h_g = 87.35

x= 0.3

h₁ = h_v + x ( h_g - h_f )

h₁ = -61.24 + 0.3 ( 87.35 - ( - 61.24 ) )

h₁ = -16.663

h₂ = 100.375

change in enthalapy = h₂ - h₁ = 100.375 - ( - 16.663 ) ) = 117.038

4.)

Now system undergoes constant pressure P= 500 Kpa

as it is compressed to original volume V = 0.5 m³

v₃ = V/m = 0.5 / 65 =  0.0076954

v₃ = 0.00769

At pressure = 500 KPa from steam tables saturated

interpolate for p = 500 in tables

500 = 360.8 + x ( 541.1 - 360.8 )

x=0.772

v_f = 0.001343 + 0.772 ( 0.001393 - 0.001343)

v_f = 0.0013816

vg = 0.06611 + 0.772 ( 0.04476 - 0.06611 )

vg = 0.0496

v = vf + x ( vg - vf )

0.00769 =  0.0013816 + x ( 0.0496 - 0.0013816 )

x = 0.1308

quality = 0.1308