Steam at 75 kPa and 8% quality is contained in a spring-loaded piston-cylinder d

Question

Steam at 75 kPa and 8% quality is contained in a spring-loaded piston-cylinder device, as shown, with an initial volume of 2 m3.
The steam is now heated until its volume is 5 m3 and its pressure is 225 kPa.
Determine the heat transferred to and the work produced by the steam during this process.

Steam at 75 kPa and 8% quality is contained in a spring-loaded piston-cylinder device, as shown, with an initial volume of 2 m3. The steam is now heated until its volume is 5 m3 and its pressure is 225 kPa. Determine the heat transferred to and the work produced by the steam during this process.

Explanation / Answer

P1 = 75kPa
P2 = 225kPa

V1= 2m^3
V2=5m^3

at P1,

u1= u_f+x_1*u_fg = 284.36+0.08*(2111.8) = 553.04 kJ/kg
v1 = v_f+x_1*v_fg = 0.001037+0.08*(2.216) = 0.17833 m^3/kg

mass of water (m) = V/v1 = 2/0.17833 = 11.215 kg
specific volume (v2) = V2/m = 5/11.215 = 0.446 m^3/kg

at P2 and v2,

x2 = v-vf/v_fg = 0.55

u2 = u_f+x*u_fg = 520.47+0.55*2012.7 = 1627.455 kJ/kg

U = m(u2-u1) = 11.215(1627.455-553.304) = 12046.600kJ

so work done (W) = (P1+P2)(V2-V1)/2 = 75+225(5-2)/2 = 450 kJ

so Q_in -W_out = U

Q_in = 12046.6 +450

Q_in = 12496.6 kJ

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