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AP Physics 2
9.4 The First Law of Thermodynamics
9.2 The Ideal Gas Law
IntermediateMCQMathematical22.4k
A horizontal rectangular cylinder with closed top, bottom, and left boundaries. Inside the cylinder on the left side, an enclosed gas region is labeled with text \(P_0, V_0\). A vertical solid rectangular piston of cross-sectional area \(A\) seals the gas on the right side. Attached to the center of the right face of the piston, a horizontal coiled spring with spring constant \(k\) extends to the right and attaches to a fixed vertical wall. A horizontal dashed line marks the initial position of the piston's right edge. A rightward arrow parallel to the cylinder indicates displacement \(x\). No other labels, lines, text, or axes appear.
Ideal gas in a cylinder with a piston attached to a spring.
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?

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