As shown in the figure below, m $=0\mathrm{.}001$ kg of air is contained in an adiabatic piston$-$cylinder apparatus that rests on a flat surface. The piston, which is massless, is attached to a spring with spring constant k $=5000$ N$/$m and a free length $$L$0=0\mathrm{.}04$ m$.$ Initially the piston is held in place by a pin. For this initial condition, the length of the spring is L$1=0\mathrm{.}1$ m$.$ The air has a volume of V$1=0\mathrm{.}004$ m$3$ and pressure of P$1=113,883$ Pa$.$ The pin is removed and the system comes to a new equilibrium state for which the spring has a new length L$2=0\mathrm{.}01$ m$,$ and the air has a volume of V$2=0\mathrm{.}006$ m$3$ and pressure of P$2=292,072$ Pa$.$ The atmosphere acting on the piston has a pressure of Patm $=105$ Pa$.$ The air can be modelled as an ideal gas with cv $=716$ J$/$kgK and R $=287$ J$/$kgK$.$

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Calculate the entropy generated $($Sgen in J$/$K$)$ in the air inside the piston$-$cylinder apparatus during the process. Provide the answer with accuracy of two decimal places."