Respuesta :
Answer:
W = -3753.8 J
[tex]W_{ideal}[/tex] = - 5163.14 J
[tex]W_{lost} = - 1409.34 \ J[/tex]
[tex]S_G = 4.70 \ \ J/K[/tex]
Explanation:
Given that:
[tex]T_1 = 500 \ K \\T_2 = 371 \ K \\T_{\sigma} = 300 \ K\\P_1 = 6 \ bar\\P_2 = 1.2 \ bar\\[/tex]
[tex]\frac{Cp}{R} = \frac{7}{2} \\n = 1[/tex]
Consider the relation
[tex]\frac{Cp}{R} = \frac{7}{2} \\[/tex]
[tex]Cp = \frac{7*R}{2}[/tex]
[tex]Cp = \frac{7*8.314 \ kJ/kmol.K}{2}[/tex]
[tex]Cp = 29.099 \ kJ/kmol.K[/tex]
Actual work W = ΔH = n Cp (T₂ - T₁)
= 1 × 29.099 (371 - 500)
= -3753.8 J
Change in entropy
ΔS = [tex]n[Cp In \frac{T_2}{T_1} - R In \frac{P_2}{P_1}][/tex]
ΔS = [tex]1*[29.099 In(\frac{371}{500}) - 8.314 In (\frac{1.2}{6})][/tex]
ΔS = 4.6978 J/K
Ideal Work
[tex]W_{ideal} = \delta H - T_{\sigma} \delta S[/tex]
= -3753.8 - 300 ( 4.6978)
= - 5163.14 J
Work lost
[tex]W_{lost} = |W_{ideal}-W|[/tex]
[tex]W_{lost} = |-5163.14 -(-3753.8)|[/tex]
[tex]W_{lost} = - 1409.34 \ J[/tex]
Entropy Generation rate:
[tex]S_G = \frac{W_{lost}}{T_{\sigma}}[/tex]
[tex]S_G = \frac{1409.34}{300}[/tex]
[tex]S_G = 4.70 \ \ J/K[/tex]
The ideal work, work lost and entropy generation rate are; W_ideal = -5163 J; W_lost = 1409.3 J; S_g = 4.698 J/K
What is the change in entropy?
We are given;
Temperature of surrounding; Tσ = 300 Κ
Temperature at initial condition; Τ₁ = 500 Κ
Pressure at initial condition; P₁ = 6 bar
Temperature at final condition; Τ₂ = 371 Κ
Pressure at final condition; P₂ = 1.2 bar
Cp/R = 7/2. where R = 8.314 kJ/mol.k
Thus; Cp = 29.099 kJ/mol
Actual work is;
W_actual = ΔH = n*Cp (T₂ - T₁)
ΔH = 1 × 29.099 × (371 - 500)
ΔH = -3753.8 J
Change in entropy is gotten from the formula;
ΔS = n[Cp In (T₂/T₁) - R In (P₂/P₁)]
Plugging in relevant values and solving gives us;
ΔS = 4.698 J/K
Ideal work is gotten from;
W_ideal = ∆H - Tσ*∆S
W_ideal = -3753.8 - (300 * 4.698)
W_ideal = -5163 J
Work Lost;
W_lost = |W_ideal - W_actual|
W_lost = |-5163 - (-3753.8)|
Solving and taking absolute value gives;
W_lost = 1409.3 J
Entropy generation rate is;
S_g = W_lost/Tσ
S_g = 1409.3/300
S_g = 4.698 J/K
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