Final answer:
To calculate the efficiency and specific work output of a gas turbine plant on the Brayton cycle, one must use formulas integrating the system's temperatures, pressure ratio, and isentropic efficiencies. Efficiency is the work output over energy input, while specific work output is based on the net work of the cycle on a P-V diagram.
Step-by-step explanation:
To calculate the efficiency and specific work output of a simple gas turbine plant operating on the Brayton cycle, it is important to understand several fundamental concepts. The efficiency of such an engine is defined as the ratio of work output to the energy input. In the context of a heat engine, this is often represented by the formula Eff = W / Qh, where W stands for the work done by the system and Qh represents the heat transfer from the hot reservoir.
Specifically, the formula for efficiency in terms of the Brayton cycle involving temperatures, pressure ratio (P1/P2), and sentropic efficiencies (represented by γ or gamma for an ideal gas) can be expressed as Eff = 1 - (P1/P2)^((γ-1)/γ). The specific work output, on the other hand, relates to the work done per unit mass and is found from the area within the cycle on a P-V diagram, which represents the net work output.
In practical terms, engineers need to consider the heat transfer during the cycle, represented as Qc during the cooling phase, and the maximum theoretical efficiency given by the Carnot cycle, which is a function of the absolute temperatures of the hot and cold reservoirs, converted to Kelvins. The real engine has limitations and often operates at an efficiency lower than this theoretical limit due to various losses and non-ideal behaviour.