What equation is used to calculate the efficiency of a thermodynamic cycle?

The equation for calculating the efficiency of a thermodynamic cycle is defined as the ratio of the work output to the heat input. Efficiency is a measure of how effectively a thermodynamic cycle converts heat energy into work. In essence, it helps in assessing the performance of heat engines.

When a working fluid absorbs heat from a high-temperature source (often denoted as Q_in), it is then used to do work (W_out) as it passes through the cycle. The efficiency can be calculated by taking the output work done by the system and dividing it by the heat input into the system. This relationship confirms that the higher the useful work output relative to the heat input, the more efficient the thermodynamic cycle is.

Heat engines typically do not operate at 100% efficiency due to various inevitable losses, such as heat lost to the surroundings or internal friction. This formulation emphasizes the importance of maximizing work output while minimizing wasted energy input.

In terms of the other options, they either misrepresent the relationship between work and heat for efficiency calculations or do not align with the fundamental definitions of thermodynamics as they pertain to engine performance metrics.