The efficiency of a Carnot cycle can be calculated using the formula:
Efficiency = 1 - (T_cold / T_hot)
Where T_cold is the temperature of the cold reservoir and T_hot is the temperature of the hot reservoir. In this case, the boiler pressure corresponds to the hot reservoir and the condenser pressure corresponds to the cold reservoir.
To find the temperatures, we can use the saturation tables for steam. At a boiler pressure of 6 MPa, dry saturated steam has a corresponding temperature of approximately 275.6°C. At a condenser pressure of 5 kPa, the corresponding temperature is approximately 41.9°C.
Converting these temperatures to Kelvin:
T_cold = 41.9°C + 273.15 = 315.05 K T_hot = 275.6°C + 273.15 = 548.75 K
Now we can calculate the efficiency:
Efficiency = 1 - (T_cold / T_hot) = 1 - (315.05 K / 548.75 K) ≈ 1 - 0.5737 ≈ 0.4263 (or 42.63%)
Therefore, the efficiency of the Carnot cycle for the given steam power plant is approximately 42.63%.