Answer:
The correct answer is i) 50.2 % ii) 13440.906 kW and iii) 71.986 kg/s.
Explanation:
In order to find the mass flow rate of the combustion of gases, there is a need to use the energy balance equation:
Mass of water × specific heat of water (T2 -T1)w = mass of gas × specific heat of gas (T2-T1)g
100 × 4.18 × [(240 + 273) - (150 + 273)] = mass of gas × 1.005 × [(1067+273) - (547+273)]
Mass of gas = 71.986 kg/s
The entropy generation of water can be determined by using the formula,
(ΔS)w = mass of water × specific heat of water ln(T2/T1)w
= 100 × 4.18 ln(513/423)
= 80.6337 kW/K
Similarly the entropy generation of water will be,
(ΔS)g = mass of gas × specific heat of gas ln(T2/T1)g
= 71.986 × 1.005 ln (820/1340)
= -35.53 kW/K
The rate of energy destruction will be,
Rate of energy destruction = To (ΔS)gen
= T₀ [(ΔS)w + (ΔS)g]
= (25+273) [80.6337-53.53)
Rate of energy destruction = 13440.906 kW
The availability of water will be calculated as,
= mass of water (specific heat of water) [(T₁-T₂) -T₀ ln T₁/T₂]
= 100 × 4.8 [(513-423) - 298 ln 513/423]
= 13591.1477 kW
The availability of gas will be calculated as,
= mass of gas (specific heat of gas) [(T₁-T₂) - T₀ ln T₁/T₂]
= 71.986 × 1.005 × [(1340-820) - 298 ln 1340/820]
= 27031.7728 kW
The exergetic efficiency can be calculated as,
= Gain of availability / loss of availability
= 13591.1477/27031.7728
= 0.502
The exergetic efficiency is 50.2%.
