\(\color{Blue}{Thermodynamics}\)

An expandable cylinder has its top connected to a spring with force constant \(2\times { 10 }^{ 3 }\text{ N/m}\) The cylinder is filled with \(5.00 \text{ L}\) of gas with the spring relaxed at a pressure of \(1.00\text{ atm}\) and a temperature of \(20.0^\circ C\). If the lid has a cross-sectional area of \(0.01 \text{ m }^{ 2 }\) and negligible mass, how high will the lid rise when the temperature is raised to \(250^\circ C\)?

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