An ideal heat engine working between temperatures $T_1$ and $T_2$ has an efficiency ;$\eta$ . The new efficiency if the temperatures of both the source and sink are doubled, will be& ;

Efficiency of heat engine $\eta=\dfrac{output}{input}=\dfrac{{T}_{1}-{T}_{2}}{{T}_{1}}$-------(a)

Now new efficiency of heat engine when sin and source temperature is doubled${\eta}_{new}=\dfrac{2{T}_{1}-2{T}_{2}}{2{T}_{1}}$

${\eta}_{new}=\dfrac{2 ({T}_{1}-{T}_{2})}{2{T}_{1}}=\eta$ from a