Question

A cylinder contains ethylene, C2H4, at 1.536 MPa, -13oC. It is now compressed in a reversible isobaric (constant pressure) process to saturated liquid. Find the specific work, heat transfer and entropy generated.

Answer 1

Ethylene C2 H4 ;

P1 = 1.536 MPa = P2 , T1 = -13o C = 260.2 K

State 2: saturated liquid, x2 = 0.0  

Tr1 =  260.2 / 282.4 = 0.921

Pr1 = Pr2 =   = 1.536 / 5.04 = 0.305

from compressibility factor chart

Z1 = 0.85 ,

(h*₁-h₁ )/RTc = 0.40

v1 = Z1 * R *T1 / P1 =  0.85×0.29637×260.2 / 1536 =  0.042675

(h*1-h₁ ) = 0.296 37×282.4×0.40 = 33.5

from compressibility factor chart

T₂ = 0.824×282.4 = 232.7 K  

Z₂ = 0.05  

(h* 2-h2 )/RTc = 4.42

v2 = Z2 *R*T2 / P2 = 0.05×0.29637×232.7 / 1536 = 0.002245

(h* 2-h2 ) = 0.296 37×282.4×4.42 = 369.9

(h* 2-h* 1) = C_PO(T2 -T1 ) = 1.5482(232.7-260.2) = -42.6

w₁₂ = ?? Pdv = P(v2 -v1 ) = 1536(0.002 245-0.042 675) = -62.1 kJ/kg

q₁₂ = (u2 -u1 ) + w₁₂ = (h2 -h1 ) = -369.9 - 42.6 + 33.5 = -379 kJ/kg

rate of entropy generated

S_gen = C_p*(ln(T2 / T1 )

= 1.5482 * ( ln (232.7 / 260.2 ) )

= -0.17293 KJ/Kg K