An ideal gas is enclosed in a horizontal cylinder fitted with a frictionless piston of cross-sectional area \(A\). Initially, the gas is at pressure \(P_0\) and volume \(V_0\), and an uncompressed spring with spring constant \(k\) is attached to the outer face of the piston. Heat is slowly transferred to the gas, causing it to expand and push the piston outward by a distance \(x\). Assuming external atmospheric pressure is negligible, what is the total work done by the gas on the piston during this expansion?