Answer
$870^{\circ} C$.
Work Step by Step
The maximum efficiency (Carnot efficiency) is given by equation 15–5. Make sure to measure temperatures in kelvins. Find the exhaust temperature from the original Carnot efficiency of 0.22.
$$e_{ideal}=1-\frac{T_L}{T_H}$$
$$T_L=T_H(1-e)=( 580+273K)(1-0.22)=665.1\;K $$
Now calculate the new intake temperature for the desired Carnot efficiency of 0.42, using the exhaust temperature of 665.1 K.
$$e_{ideal}=1-\frac{T_L}{T_H}$$
$$T_H=\frac{T_L}{1-e}=\frac{665.1+273K}{1-0.42}=1147\;K\approx870^{\circ} C $$
