1. The problem statement, all variables and given/known data An expandable cylinder has its top connected to a spring of constant 2000 N/m. The cylinder is filled with 5L of gas with the spring relaxed at a pressure of 1 atmosphere and a temperature of 20C. If the lid has a cross-sectional area of 0.01m2 and negligible mass, how high will the lid rise when the temperature is raised to to 250C? 2. Relevant equations PV = nRT PV/T initial = PV/T final 3. The attempt at a solution P = Force/Area. When the gas expands it pushes on the spring which pushes back with F = k * displacement. Displacement here is h so P=kh/A. We already know the initial pressure is 1 atmosphere, so the final P is kh/A + 1. The initial volume is 5L, so the final volume must be 5 + Ah. The initial temperature and final temperature are given as 20 and 250C. Plugging that in gives: (1*5)/20 = (1 + kh/A)(5 + Ah)/250 62.5 = (1 + kh/A)(5 + Ah) which yields a quadratic: 62.5 = 5 + Ah + 5kh/A + kh2 Ah = .01h and 5kh/A = 106h so Ah can be neglected when adding these terms ≈ 106h. 0 = -57.5 + 106h + 2000h2 When I solve this quadratic equation I get h = 5.75E-5. But this isn't the right answer. I'm stuck on figuring out where I went wrong so help is very appreciated. Thank you!