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In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is compressed to 6 atm and the maximum cycle temperature is limited to 1100 K by using large air fuel ratio. If the heat supply is 100 MW, find the thermal efficiency of the cycle and also the work ratio.?
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In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is...
Brayton Cycle
The Brayton cycle is a thermodynamic cycle used in gas turbine engines and some air compressor systems. It consists of four processes: isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection.
Given Parameters
- Inlet Pressure (P1) = 1 atm
- Inlet Temperature (T1) = 300 K
- Outlet Pressure (P2) = 6 atm
- Maximum Cycle Temperature (T3) = 1100 K
- Heat Supply (Qin) = 100 MW
Thermal Efficiency
The thermal efficiency of the Brayton cycle can be calculated using the formula:
η = (Net Work Output / Heat Supply) = (Wturbine - Wcompressor) / Qin
Where,
- Wturbine = Work done by the turbine
- Wcompressor = Work done by the compressor
Calculating Wcompressor
The compression process is isentropic, so we can use the isentropic compression equation to calculate the work done by the compressor:
Wcompressor = C_p * T1 * [(P2/P1)^((γ-1)/γ) - 1]
Where,
- C_p = Specific heat at constant pressure
- γ = Ratio of specific heats
Substituting the given values, we get Wcompressor = 192.5 MW
Calculating Wturbine
The expansion process is also isentropic, so we can use the isentropic expansion equation to calculate the work done by the turbine:
Wturbine = C_p * T3 * [(P2/P1)^((γ-1)/γ) - 1]
Substituting the given values, we get Wturbine = 370.7 MW
Calculating Thermal Efficiency
Substituting the values of Wcompressor and Wturbine in the formula of thermal efficiency, we get:
η = (Wturbine - Wcompressor) / Qin = (370.7 - 192.5) / 100 = 178.2 / 100 = 1.782
Therefore, the thermal efficiency of the cycle is 1.782 or 178.2%.
Work Ratio
The work ratio is defined as the ratio of the turbine work to the compressor work:
WR = Wturbine / Wcompressor = 370.7 / 192.5 = 1.925
Therefore, the work ratio of the cycle is 1.925.
The Brayton cycle is a thermodynamic cycle used in gas turbine engines and some air compressor systems. It consists of four processes: isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection.
Given Parameters
- Inlet Pressure (P1) = 1 atm
- Inlet Temperature (T1) = 300 K
- Outlet Pressure (P2) = 6 atm
- Maximum Cycle Temperature (T3) = 1100 K
- Heat Supply (Qin) = 100 MW
Thermal Efficiency
The thermal efficiency of the Brayton cycle can be calculated using the formula:
η = (Net Work Output / Heat Supply) = (Wturbine - Wcompressor) / Qin
Where,
- Wturbine = Work done by the turbine
- Wcompressor = Work done by the compressor
Calculating Wcompressor
The compression process is isentropic, so we can use the isentropic compression equation to calculate the work done by the compressor:
Wcompressor = C_p * T1 * [(P2/P1)^((γ-1)/γ) - 1]
Where,
- C_p = Specific heat at constant pressure
- γ = Ratio of specific heats
Substituting the given values, we get Wcompressor = 192.5 MW
Calculating Wturbine
The expansion process is also isentropic, so we can use the isentropic expansion equation to calculate the work done by the turbine:
Wturbine = C_p * T3 * [(P2/P1)^((γ-1)/γ) - 1]
Substituting the given values, we get Wturbine = 370.7 MW
Calculating Thermal Efficiency
Substituting the values of Wcompressor and Wturbine in the formula of thermal efficiency, we get:
η = (Wturbine - Wcompressor) / Qin = (370.7 - 192.5) / 100 = 178.2 / 100 = 1.782
Therefore, the thermal efficiency of the cycle is 1.782 or 178.2%.
Work Ratio
The work ratio is defined as the ratio of the turbine work to the compressor work:
WR = Wturbine / Wcompressor = 370.7 / 192.5 = 1.925
Therefore, the work ratio of the cycle is 1.925.
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In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is compressed to 6 atm and the maximum cycle temperature is limited to 1100 K by using large air fuel ratio. If the heat supply is 100 MW, find the thermal efficiency of the cycle and also the work ratio.?
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In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is compressed to 6 atm and the maximum cycle temperature is limited to 1100 K by using large air fuel ratio. If the heat supply is 100 MW, find the thermal efficiency of the cycle and also the work ratio.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is compressed to 6 atm and the maximum cycle temperature is limited to 1100 K by using large air fuel ratio. If the heat supply is 100 MW, find the thermal efficiency of the cycle and also the work ratio.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is compressed to 6 atm and the maximum cycle temperature is limited to 1100 K by using large air fuel ratio. If the heat supply is 100 MW, find the thermal efficiency of the cycle and also the work ratio.?.
In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is compressed to 6 atm and the maximum cycle temperature is limited to 1100 K by using large air fuel ratio. If the heat supply is 100 MW, find the thermal efficiency of the cycle and also the work ratio.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is compressed to 6 atm and the maximum cycle temperature is limited to 1100 K by using large air fuel ratio. If the heat supply is 100 MW, find the thermal efficiency of the cycle and also the work ratio.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an ideal Brayton cycle , air from the atmosphere at 1 atm, 300 K is compressed to 6 atm and the maximum cycle temperature is limited to 1100 K by using large air fuel ratio. If the heat supply is 100 MW, find the thermal efficiency of the cycle and also the work ratio.?.
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