In an ideal Brayton cycle, air from the atmosphere at 1atm,300 K is compressed to 6 atm and the maximum cycle temperature is limited 1100 K by using a large air fuel ratio. If the heat supply is 100 MW, find (a) the thermal efficiency of the cycle (b) work ratio (c) power output.?

Given data:
- Atmospheric pressure = 1 atm
- Atmospheric temperature = 300 K
- Compressed pressure = 6 atm
- Maximum cycle temperature = 1100 K
- Heat supply = 100 MW

(a) Thermal Efficiency of the Cycle:
- The thermal efficiency of the Brayton cycle is given by the formula:
η = (1 - (1/r)^(γ-1)) x (T3 - T2) / (T4 - T1)
where, r = P2/P1 (pressure ratio)
γ = Cp/Cv (specific heat ratio)
T1 = atmospheric temperature
T2 = temperature after compression
T3 = maximum cycle temperature
T4 = temperature after expansion
- From the given data, we can calculate:
r = 6/1 = 6
γ = 1.4 (for air)
T1 = 300 K
T2 = T1 x r^(γ-1) = 300 x 6^(1.4-1) = 1194.8 K
T4 = T3 x r^(-γ) = 1100 x 6^(-1.4) = 384.8 K
- Substituting the values in the formula, we get:
η = (1 - (1/6)^(1.4-1)) x (1100 - 1194.8) / (384.8 - 300)
η = 0.38 or 38%

(b) Work Ratio:
- The work ratio of the Brayton cycle is given by the formula:
WR = (T3 - T2) / (T4 - T1)
- Substituting the values from the given data, we get:
WR = (1100 - 1194.8) / (384.8 - 300)
WR = -0.63 or 63% (negative sign indicates that work is being done on the cycle)

(c) Power Output:
- The power output of the Brayton cycle is given by the formula:
P = Q / η
where, Q = heat supply
η = thermal efficiency
- Substituting the values from the given data, we get:
P = 100 / 0.38
P = 263.15 MW


Explanation:
The problem requires to find the thermal efficiency, work ratio, and power output of an ideal Brayton cycle. The Brayton cycle is a thermodynamic cycle that describes the functioning of a gas turbine engine. In this cycle, air from the atmosphere is compressed, heated at a constant pressure, expanded, and then cooled back to its initial state. The cycle consists of four processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant pressure heat rejection. The ideal Brayton cycle assumes that these processes are reversible and adiabatic, and that there are no losses due to friction or other inefficiencies.

To solve the problem, we first need to calculate the values of pressure ratio (r), specific heat ratio (γ), temperature after compression (T2), and temperature after expansion (T4). These values can be calculated using the given data. Once we have these values, we can use the formulas for thermal efficiency, work ratio,