A sealed, frictionless, vertical piston contains a fixed amount of ideal gas. Starting from state 1, additional small masses are gently placed on the piston so that the gas is compressed quasistatically while remaining in thermal contact with a large reservoir that maintains its temperature at a constant value T0. The process ends at state 2 when the pressure of the gas has doubled.
Answer the following questions about this experiment and a related comparison experiment.
(a) Describe qualitatively how the pressure and volume of the gas change during the compression from state 1 to state 2.
(b) On axes with pressure on the vertical axis and volume on the horizontal axis, sketch the expected curve that represents the path from state 1 to state 2. Label both states clearly.
(c) Explain why the signed area under the curve you sketched corresponds to the work done on or by the gas during this process.
(d) A second experiment begins from the same state 1, but instead the gas is heated at constant volume until its pressure equals the pressure at state 2. Compare the magnitudes of the temperature changes in the two experiments and justify your answer using proportional reasoning.