A hydrostatic system consists of 0.1 moles of an ideal gas whosespecific heat capacity at constant volume, ??, is equal to 3?2where R is the gas constant equal to 8.31 J mol–1 K–1. Its initialpressure and volume are 32 Pa and 8 m3. In its final state, thepressure is just 1 Pa and its volume increases eightfold. Theparticular thermodynamic process can be represented on an indicatordiagram as a straight line joining the initial and finalstates.
(a) Determine a relationship between the pressure and the volume ofthe gas that represents the thermodynamic process.

(b) Establish a relationship between the temperature and the volumeof the gas valid for the thermodynamic process.

(c) Determine the volume of the gas when the temperature is amaximum.

(d) Determine the temperature of the gas at the initial and finalstates, and the maximum temperature attained by the gas in theprocess.

(e) Imagine that the gas, while following the thermodynamic processoutlined above, is at some arbitrary state such that its volume isV. This state is somewhere between the initial and final states.Determine the heat exchange that occurs while the gas is traversing(along the process) from the initial to the arbitrary state. Yourexpression should be a function of V only.

(f) With reference to part (e), determine that volume whichcorresponds to maximum heat exchange. Hence determine thecorresponding temperature.