# $$\color{Blue}{Thermodynamics}$$

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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