$\color{#3D99F6}{Thermodynamics}$

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 $250^\circ C$ ?