$"$As shown in the figure below, $m=0\mathrm{.}005kg$ 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 $k=5000\frac{N}{m}$ and a free length $LO=0\mathrm{.}04m.$ Initially the piston is held in place by a pin with the air in an unknown initial state. For this initial the a spring is $L1=0\mathrm{.}137m.$ The pin is removed and the system comes to a new equilibrium state for which the spring has a new length $L2=0\mathrm{.}016m$ and the air has a volume of $V2=0\mathrm{.}005m^3.$ The piston has an area $A=0\mathrm{.}004m^2.$ Assume $P_{\text{a}\text{t}\text{m}}={10}^{5}Pa.$ The air can be modelled as an ideal gas with $c_V=716\frac{J}{k}gK$ and $R=287\frac{J}{k}gK.$ Calculate the work by the system on the environment in J$.$ Provide the answer as a whole number $($zero decimal places$)."$