# Does the second law of thermodynamics put limit on efficiency of engines?

In thermodynamics it is claimed that the efficiency of no engine can be one. But look at the efficiency of let's say Carnot engine $\eta=1-T_c/T_h$. Now one can take $T_c$ arbitrarily close to absolute zero then make the efficiency of the engine close to one? So indeed it is possible to have efficiency at least close to one !!?

The second law just says that the efficiency of any engine operating between two reservoirs with temperature $T_H$ and $T_C$ cannot exceed the Carnot efficency $$e_c=1-\frac{T_C}{T_H}$$.
Besides, $T_C$ cannot be zero by the third law of thermodynamics.
Also, in principle the efficiency can be greater than $1$ if temperature can be negative.
However, in that case the definition of $$\text{efficiency}=\frac{W}{Q_H}$$ may not make sense.