$2-$ The heat engine shown in the image is working between a $400gh$ temperature reservoir and a $40C$ low temperature reservoir. $110$ kW of thermal power is being transferred to the heat engine from the high temperature reservoir.

a$)$ Find the output mechanical power and the efficiency of the heat engine, if $60$ kW of thermal power is being transferred to low temperature reservoir. $(5$ points$)$

b$)$ Find maximum efficiency a heat engine that can work between these two reservoirs. $(3$ points$)$

c$)$ Find the increase in the output mechanical power $($for the same $110$ kW input thermal power$),$ when a reversible cycle heat engine is used. $(2$ points$)$