A preliminary study on graphical method of thermodynamic process parameters under dynamic boundary conditions

<p>Thermodynamic graphical methods are useful tools for visualizing thermodynamic state equations and are widely applied in the design and optimization of thermodynamic systems. However, the integration of renewable energy and thermal storage systems introduces finite heat capacity characteristics, resulting in continuous dynamic variations in system performance, which poses challenges to existing graphical methods. To accurately describe system performance under dynamic boundary conditions, this study investigates the continuous analysis characteristics of the Energy-Energy (<i>E</i>-<i>E</i>) diagram. Based on the ideal gas model, mathematical expressions for thermal and mechanical energy are derived, and systematic comparisons between <i>E</i>-<i>E</i> and Temperature (<i>T</i>)-Entropy (<i>s</i>) diagrams under finite heat capacity conditions are conducted, elucidating the intrinsic relationships among geometric parameters, initial boundary conditions, and system performance. Through parametric analysis, we reveal that increasing the initial heat reservoir temperature from 500 K to <styled-content style-type="number">1500</styled-content> K enhances the energy conversion potential, with the rotation angle increasing from 20.77° to 37.15°. Additionally, increasing the heat reservoir to cold reservoir capacity ratio results in a decreased rotation angle, indicating lower efficiency. The <i>E</i>-<i>E</i> diagram achieves visualization by analogizing energy conversion processes to the rotational motion of a radius in a circle. Compared to the <i>T</i>-<i>s</i> diagram, it employs lines and slopes instead of areas and area ratios, exhibiting advantages in analyzing varying boundary conditions. This complementary coupling provides a new perspective for describing dynamic energy conversion processes in thermodynamic systems.</p>