Consider a hypothetical heat engine that, in a cycle, takes $100$ J of thermal energy from a hot reservoir at $500$ K$,$ dumps $50$ J into a cold reservoir at $300$ K$,$ and performs $50$ J of work. Which of the following is true? $($Choose all that apply.$)$

In each cycle, the entropy of the cold reservoir increases by $0\mathrm{.}2$ J$/$K

With these reservoir temperatures, this is the maximum possible efficiency you could get from any heat engine

With these reservoir temperatures, the Carnot efficiency equals $60\%($or $0\mathrm{.}6)$

With these reservoir temperatures, the Carnot efficiency equals $40\%($or $0\mathrm{.}4)$

In each cycle, the entropy of the hot reservoir decreases by $0\mathrm{.}17$ J$/$K

In each cycle, the entropy of the hot reservoir decreases by $0\mathrm{.}2$ J$/$K

In each cycle, the entropy of the cold reservoir increases by $0\mathrm{.}17$ J$/$K

This engine is impossible because it violates the second law of thermodynamics

The efficiency of this engine is $50\%($or $0\mathrm{.}5)$