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Efficiency of the Carnot鈥檚 engine is the ratio of work done by the engine to the heat intake from the hot body. The maximum efficiency of the Carnot鈥檚 engine is given by the formula

\({\bf{\eta = 1 - }}\frac{{{{\bf{T}}_{\bf{c}}}}}{{{{\bf{T}}_{\bf{h}}}}}\)

Here,

\(\eta \)- efficiency of the engine.

\({T_c}\)- the temperature of the cold reservoir.

\({T_h}\)- temperature of the hot reservoir

Temperature of cold reservoir\({T_c} = 20{\;^{\rm{o}}}{\rm{C}} = 293\;{\rm{K}}\)

Temperature of hot reservoir\({T_h} = 550{\;^{\rm{o}}}{\rm{C}} = 823\;{\rm{K}}\)

The efficiency of the Carnot engine \(\eta = 1 - \frac{{{T_c}}}{{{T_h}}}\)

Maximum efficiency can be calculated by calculating Carnot efficiency as

\(\begin{aligned}{}\eta &= 1 - \frac{{{T_c}}}{{{T_h}}}\\ &= 1 - \frac{{293\;}}{{823}}\\ &= 0.644\\ &= 64.4\% \end{aligned}\)

Real efficiency\({\eta _1} = 38\% \)

Percentage real efficiency is of maximum efficiency \(\left( {N\% } \right)\)

\(\begin{aligned}{}N\% & = (38\% /64.4\% ) \times 100\\ &= 59\% \end{aligned}\)

Therefore, the maximum efficiency is \(64.4\% \)for the station. The real efficiency is \(59\% \) of the Carnot efficiency.