A Brayton Gas turbine cycle produces 14 MW with an inlet state of the compressor is T10C, P1 kPa, and a compression ratio of rP. The heat added in the combustion is 960 kJ/kg. Determine the specific compressor work.Where,T1=190CP1= 118 kParP=14:1Specific heat at a constant pressure of air, CP= 1.004 kJ/kg kPolytropic Index, n for compressor, turbine and combustion chamber=1.4
Question
A Brayton Gas turbine cycle produces 14 MW with an inlet state of the compressor is T10C, P1 kPa, and a compression ratio of rP. The heat added in the combustion is 960 kJ/kg. Determine the specific compressor work.Where,T1=190CP1= 118 kParP=14:1Specific heat at a constant pressure of air, CP= 1.004 kJ/kg kPolytropic Index, n for compressor, turbine and combustion chamber=1.4
Solution
Given:
T1 = 190C = 190 + 273 = 463 K (Converted from Celsius to Kelvin) P1 = 118 kPa rP = 14:1 CP = 1.004 kJ/kg K n = 1.4
We need to find the specific compressor work (Wc).
The formula for the specific compressor work is:
Wc = CP * T1 * [(P2/P1)^((n-1)/n) - 1]
Where P2 is the pressure after compression. Given the compression ratio (rP) is 14:1, we can say P2 = rP * P1 = 14 * 118 = 1652 kPa.
Substituting the given values into the formula, we get:
Wc = 1.004 kJ/kg K * 463 K * [(1652/118)^((1.4-1)/1.4) - 1]
Solving this will give us the specific compressor work.
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