Explain why the efficiency of a Carnot engine cannot be $100\%$?

(N/A) The efficiency of a Carnot engine is given by the formula $\eta = 1 - \frac{T_L}{T_H}$,where $T_L$ is the absolute temperature of the cold reservoir (sink) and $T_H$ is the absolute temperature of the hot reservoir (source).
For the efficiency $\eta$ to be $100\%$ (or $1$),the term $\frac{T_L}{T_H}$ must be equal to $0$.
This implies that either $T_L = 0 \ K$ (absolute zero) or $T_H = \infty$.
According to the Third Law of Thermodynamics,it is impossible to reach absolute zero $(0 \ K)$ in a finite number of steps.
Furthermore,it is physically impossible to have a heat source at infinite temperature.
Therefore,it is impossible for any heat engine,including the ideal Carnot engine,to have an efficiency of $100\%$.