Carnot engine: A Carnot engine operating between a reservoir of liquid mercury at its melting point $(233$ K$)$ and a colder reservoir extracts $10\mathrm{.}0$ J of heat from the mercury and does $8\mathrm{.}0$ J of work during each cycle. What is the temperature of the colder reservoir?$$

A$)47$ K$$

B$)186$ K$$

C$)163$ K$$

D$)207$ K$$