For all heat engines, the maximum work output (W) is related to the maximum heat input energy (Q) by the following equation:
thermodynamics problems carnot effiency equation
where TH is the temperature of the heat source, and TL is the temperature of the heat sink, which is the temperature of the "leftover" heat energy after work is extracted from the process. Both temperatures are in units of Kelvin.
The term inside the brackets represents the thermal efficiency of the process, commonly known as the Carnot efficiency.
In an application involving a Stirling engine (a type of heat engine, shown below), a parabolic dish is used to concentrate solar energy onto the receiver of the engine. Using the equation above, why would this produce more power output than using non-concentrated solar energy as the heat source, collected over the same area as the dish.
Answers
According to the equation for Carnot efficiency, a greater temperature difference between heat source and heat sink results in greater power output (higher thermal efficiency). And a lower temperature difference results in lower power output (lower thermal efficiency). This is why, for purposes of solar thermal power generation, it is desirable to focus sunlight from a large area onto a small area. The result is much higher temperature for the heat source and much higher thermal efficiency as a result, which means much higher power output for the engine. For example, a collector of surface area A that is collecting heat energy from the sun to run a heat engine, is much less efficient (and produces much less power) than a heat engine that uses that same energy, but in concentrated form. In other words, focusing the sunlight impinging on A onto a small point and using that energy to run a heat engine is much more efficient and produces more power than using unfocused sunlight falling on the collector. The more you can focus the heat energy the more power you will get. This is why Stirling dishes, which focus sunlight to a point, produce more power than parabolic troughs, which focus sunlight along a line (assuming both use the same area of sun exposure). The focal temperature is higher in the Stirling dishes than in parabolic troughs, which is why they are more efficient.