An ideal gas is contained within a cylinder sealed at one end and equipped at the other end with a frictionless piston, of cross-sectional area a and exposed on its outer face to the ambient atmosphere, assumed to remain at a fixed pressure po. in complete thermodynamic equilibrium, the piston is located a distance lo from the closed, fixed end. suppose the gas is compressed (or rarefied) by displacing the piston by r from its equilibrium location. ignoring gravity and assuming the piston always moves quasi-statically, find the restoring force on the piston under such a displacement, assuming (a) the cylinder is immersed in a heat bath at temperature to; or (b) the cylinder and piston are instead thermally insulated (c) can you think of any situations where such a system might be preferred to standard steel spring? why? would it actually be possible to thermally but not mechanically isolate the piston, as in part (b)?