The efficiency of a reversible power cycle can be calculated using the formula:
Efficency (η) = 1 – (Tc / Th)
In this case, Th (the temperature of the hot reservoir) is 1200 K and Tc (the temperature of the cold reservoir) is 300 K. Plugging in these values:
η = 1 – (300 K / 1200 K)
η = 1 – 0.25
η = 0.75
This means that the efficiency of the power cycle is 0.75 or 75%.
In simpler terms, this means that 75% of the energy taken from the hot reservoir is converted into work, while 25% is rejected to the cold reservoir. This high efficiency is characteristic of reversible power cycles, which ideally operate without any energy loss.