Answer:
a) the amount of energy produced in kJ/K is 0.73145 kJ/K
b) the amount of energy produced in kJ/K is 0.68975 kJ/K
The value for entropy production obtained using constant specific heats is approximately 6% higher than the value obtained when accounting explicitly for the variation in specific heats.
Explanation:
Draw the T-s diagram.
a)
= 0.939 kJ/kg.K , m = 5 kg , T₂ = 520 K , T₁ = 280
R = [8.314 kJ / 44.01 kg.K] , P₂ = 20 bar , P₁ = 2 bar
Δs = ![m[c_p ln(\frac{T_2}{T_1}) - Rln(\frac{P_2}{P_1})]](https://tex.z-dn.net/?f=m%5Bc_p%20ln%28%5Cfrac%7BT_2%7D%7BT_1%7D%29%20-%20Rln%28%5Cfrac%7BP_2%7D%7BP_1%7D%29%5D)
Substitute all parameters in the equation
Δs = ![5[(0.939) ln(\frac{520}{280}) - (\frac{8.314}{44.01})ln(\frac{20}{2})]](https://tex.z-dn.net/?f=5%5B%280.939%29%20ln%28%5Cfrac%7B520%7D%7B280%7D%29%20-%20%28%5Cfrac%7B8.314%7D%7B44.01%7D%29ln%28%5Cfrac%7B20%7D%7B2%7D%29%5D)
Δs = 5 kg × 0.14629 kJ/kg.K
= 0.73145 kJ/K
b)
Δs = ![m[\frac{s^0(T_2) - s^0(T_1)}{M} - Rln(\frac{P_2}{P_1})]](https://tex.z-dn.net/?f=m%5B%5Cfrac%7Bs%5E0%28T_2%29%20-%20s%5E0%28T_1%29%7D%7BM%7D%20-%20Rln%28%5Cfrac%7BP_2%7D%7BP_1%7D%29%5D)
Where T₁ = 280 K , s°(T₁) = 211.376 kJ/kmol.K
T₂ = 520 K , s°(T₂) = 236.575 kJ/kmol.K
R = [8.314 kJ / 44.01 kg.K] , M = 44.01 kg.K , P₂ = 20 bar , P₁ = 2 bar
Δs = ![5[\frac{236.575 - 211.376}{44.01} - (\frac{8.314}{44.01})ln(\frac{20}{2})]](https://tex.z-dn.net/?f=5%5B%5Cfrac%7B236.575%20-%20211.376%7D%7B44.01%7D%20-%20%28%5Cfrac%7B8.314%7D%7B44.01%7D%29ln%28%5Cfrac%7B20%7D%7B2%7D%29%5D)
= 5 kg (0.13795 kJ/kg.K)
= 0.68975 kJ/K
The value for entropy production obtained using constant specific heats is approximately 6% higher than the value obtained when accounting explicitly for the variation in specific heats.