Question

This problemdemonstrates that heat and work are dependent uponpath whileinternal energy is a state function (path independent).Considerthe isothermal expansion of one mole of an ideal gas fromaninitial state (Pinit =1atm and Tinit= 300 K) to a finalstate(Pfinal=0.1 atm, Tfinal=300K). Now this can be
accomplished by an infinite number of paths – lets considerjusttwo.

Path #1 The irreversible isothermal expansion takes place againstaconstant external pressure of 0.1atm.
Path#2 The isothermal expansion takes place in two steps, firstanirreversible expansion to the intermediate state (Pint=0.5atm,Tint=300K) against an external pressure of 0.5 atm, and nextanirreversible expansion from the intermediate state to thefinalstate against an external pressure of 0.1
atm.

a) What is the change in internal energy(ΔU=Ufinal−Uinit) for path#1? for path #2?
b) What is the work done by the system in path#1? Use the firstlawto calculate the heat absorbed by the system for path#1.
c) What is the work done by the system in path#2? (Sum up theworkfor each step). Use the first law to calculate the heatabsorbed bythe system for path#2.
d) You should have observed that the heat and work weredifferentfor each path although the change in internal energywasindependent of path. Suggest a third path which takes thesystemfrom the same initial state to the same final state.