Despite its inefficiency, the gas turbine enables our most...

Despite its inefficiency, the gas turbine enables our most efficient fossil-fueled power plant, the combined-cycle gas turbine. This system burns natural gas in a gas turbine, then uses the turbine's exhaust to drive a conventional steam cycle. Consider a system using the gas turbine of the preceding problem, with the steam cycle then operating between the turbine's $590^{\circ} \mathrm{C}$ exhaust and discharging waste heat at $42^{\circ} \mathrm{C}$. Find (a) the maximum efficiency of the steam cycle alone and (b) the maximum efficiency of the combined cycle.

Key Concepts

Combined-Cycle Power Plant

A combined?cycle power plant is a system that integrates two thermodynamic cycles, typically a gas turbine cycle with a steam cycle, to generate electricity. In such a system, the waste heat from the high?temperature gas turbine exhaust is used to produce steam for a secondary steam turbine, thereby extracting additional work from the fuel and improving overall efficiency.

Gas Turbine

A gas turbine is a type of internal combustion engine that converts the energy stored in fuel into mechanical work through the combustion of the fuel and the expansion of hot gases. In power generation, the gas turbine cycle serves as the primary cycle, and its waste heat can be reutilized in a secondary cycle, even though its own efficiency might be lower compared to that of the complete combined cycle.

Steam Cycle Efficiency

The steam cycle, often operating as a Rankine cycle in power plants, converts the thermal energy from high-temperature steam into mechanical energy using expansion in a turbine. Its efficiency is determined by the temperature difference between the steam entering the turbine and the temperature at which heat is rejected, which ideally is bounded by the maximum efficiency predicted by ideal thermodynamic cycles.

Carnot Efficiency

Carnot efficiency represents the theoretical maximum efficiency that any heat engine can achieve operating between two temperature reservoirs. It sets an upper limit based on the absolute temperatures of the heat source and the sink, and is fundamental to analyzing the performance limits of both the gas turbine and steam cycles in a combined-cycle system.

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