The criteria for the spontaneity of a process are

For an ideal gas, consider only $\mathrm{P}-\mathrm{V}$ work in going from an initial state $\mathrm{X}$ to the final state $\mathrm{Z}$. The final state $\mathrm{Z}$ can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct ? [take $∆\mathrm{S}$ as change in entropy and $\mathrm{W}$ as work done].

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

An ideal gas in a thermally insulated vessel at internal pressure =${\mathrm{P}}_1$, volume =${\mathrm{V}}_1$ and absolute temperature=${\mathrm{T}}_1$ expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of gas are${\mathrm{P}}_2$, ${\mathrm{V}}_2$ and ${\mathrm{T}}_2$ respectively.

For this expansion which of the following conditions holds correct?