A Carnot engine has efficiency of 60%. If the temperature of the sink is reduced by 800C, its efficiency increases by 20%. The temperature of source is___K.(Round off to nearest integer)

η=1−T2T1 , 0.4=T2T1 , T2=0.4T1η=1−T2T1 , 0.6+(0.2×0.6)=0.72=1−T2−80T1 , T2−80T1=0.280.4T1−80T1=0.28 , 0.4T1−0.28T1=80T1=666.67K

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A Carnot engine has efficiency of 60%. If the temperature of the sink is reduced by 80⁰C, its efficiency increases by 20%. The temperature of source is___K.
(Round off to nearest integer)

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answer is 667.

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$η = 1 - \frac{T_{2}}{T_{1}}, 0.4 = \frac{T_{2}}{T_{1}}, T_{2} = 0.4 T_{1}$

$η = 1 - \frac{T_{2}}{T_{1}}, 0.6 + (0.2 \times 0.6) = 0.72 = 1 - \frac{T_{2} - 80}{T_{1}}, \frac{T_{2} - 80}{T_{1}} = 0.28$

$\begin{array}{l} \frac{0.4 T_{1} - 80}{T_{1}} = 0.28, 0.4 T_{1} - 0.28 T_{1} = 80 \\ T_{1} = 666.67 K \end{array}$

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