(a) Efficiency of a heat engine, $\eta = 1 - \frac{T_{2}}{T_{1}}$
For $\eta = 1(i.e.,\ 100\%)$ either $T_{1} = \infty$ or $T_{2} = 0\ K$
As source at infinite temperature or sink at $0\ K$ are not attainable, therefore heat engine cannot have efficiency 1