The plot shows three different paths ($1,2,$ and $3$) connecting the initial equilibrium state $\text{X}$ to the final equilibrium state $\text{Y}$ in a thermodynamic process. Which of the following statements is/are correct?
- The change in internal energy is the same for all three paths.
- The work done is the same for all three paths.
- The heat exchange will differ depending on the path taken.
- The first law of Thermodynamics is violated if work differs along the paths.
