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Given: Carnot engine efficiency, \[{n_1} = 40\% \]

Temperature of sink, \[{T_2} = 300K\]

Efficiency increased to \[{n_2} = 60\% \]

To find:

Change in temperature of the source, now \[{T_1} = ?\]

We know efficiency of Carnot engine is

\[n = \dfrac{{{T_1} - {T_2}}}{{{T_1}}}\]

\[ \Rightarrow \,\,\,\dfrac{{40}}{{100}} = \dfrac{{{T_1} - 300}}{{{T_1}}}\]

\[ = 4{T_1} = 10T - 3000\]

\[ \Rightarrow \,\,\,6{T_1} = 3000\]

\[ \Rightarrow \,\,\,{T_1} = 500K\] is the temperature of the source initially.

Now to increase efficiency to 60%

\[{n_1} = \dfrac{{{T_1} - {T_2}}}{{{T_1}}}\]

\[\dfrac{{60}}{{100}} = \dfrac{{{T_1} = 300}}{{{T_1}}}\]

\[ \Rightarrow \,\,\,6{T_1} = 10{T_1} - 3000\]

\[ \Rightarrow \,\,\,{T_1} = 750K\] is the new source temperature.