A cylinder of height H, having a cross section S, communicates with the atmosphere using a tap (Fig.). A frictionless sliding piston is suspended from the top cover of the cylinder by a spring, which, when the tap is open, is located at a height h1 from the bottom of the cylinder. The valve closes at temperature t1 and air pressure p1. The air in the lower part of the cylinder is then heated to temperature t2; in this case, the piston is installed at a height h2 from the bottom of the cylinder. Find the spring stiffness k, assuming that the spring deformation is proportional to the acting force. The piston is considered weightless and thermally insulated.

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