Any point on the thermodynamic P V diagram below is an equilibrium state. An unknown

process, not shown on the diagram below, takes a system from equilibrium state i to equilibrium state f $.$

These two equilibrium states, and two paths between them, are shown on the P V diagram. Determine

whether the statements below are true or false and give a brief reason for your judgment.

$($a$)$ As the process may not be reversible, that is$,$ may not be through equilibrium states, the change in

internal energy, Uf $$ Ui can not be determined.

$($b$)$ The work $$ Vf

Vi P $($V $)$dV along path a is greater than the work along along path b$.$

$($c$)$ The change in internal energy along path a is greater than the change in internal energy along path

b$.$

$($d$)$ The process a shown in the gure is reversible.

$($e$)$ If we further learn that the initial and nal states are well described by the ideal gas equation of

state, then the temperature of state f is greater than the temperature of state i$.$

$($f$)$ All cyclic adiabatic processes have zero work ux$.$

$1$