For example, if we have an infinite cylinder fitted with a piston having adiabatic curved walls and a diathermal base. Now, bring the base in contact with some higher temperature body and let the cylinder absorb some heat. After that, we cover the base with an adiabatic material. Then, we let the gas to expand forever, thereby converting almost all of its energy into work by the mechanical motion of the piston. I don't understand why we have to give some heat to a lower temperature body. We can have as much efficiency as we want by letting the gas expand forever.
I wanted to ask one more thing. In my book, while explaining the efficiency of Carnot engine, there is a graph between Temperature and Entropy. The curve is cyclic and rectangular in shape. It says that the engine goes through four states $a,\ b,\ c,\ d$ corresponding to points $(T_1,S_1)$, $(T_1,S_2)$, $(T_2,S_2)$ and $(T_2,S_1)$. So, the entropy increases while going from $a$ to $b$ but decreases from $c$ to $d$. But in the same book, it was written that once entropy has been created, the universe has to carry the burden of it forever or in other words it can't be destroyed. I think that means entropy can't be decreased. Then, what did it decrease from $c$ to $d$? And why entropy can't be decreased. For example, entropy of electrons moving randomly is large but when we apply an electric field, electrons begin systematic motion and hence randomness is decreased. Then, isn't entropy destroyed"