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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 !!?

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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.

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