$($Standard solving format is required$)$ A system executes a power cycle while receiving $1000$ kJ by heat transfer at a temperature of $500$ K and discharging energy by heat transfer at a temperature of $300$ K $.$ There are no other heat transfers. If the thermal efficiency is $($a$)\backslash (100\backslash \%\backslash ),($b$)\backslash (40\backslash \%\backslash ),($c$)\backslash (25\backslash \%\backslash ),$ use $(1)$ the $2$nd Carnot corollary and $(2)$ Clausius inequality to determine whether the cycle operates reversibly, operates irreversibly, or is impossible.

Answer keys:

$($a$)$ Impossible

$($b$)$ Internally reversible

$($c$)$ Internally irreversible