A system executes a power cycle while receiving $850$ kJ by heat transfer at a temperature of $1600$ K and discharging $100$ kJ by heat transfer at a temperature of $450$ K$.$ Another heat transfer from the system occurs at a temperature of $900$ K$.$ Using the first law of thermodynamics and the Clausius inequality equation, determine the thermal efficiency if

a$)$

cycle $=0\mathrm{.}1$ kJ$/$K

b$)$

cycle $=0\mathrm{.}2$ kJ$/$K

c$)$

cycle $=0\mathrm{.}35$ kJ$/$K