Answer
Heat requirement of second Engine is $Q_2=3807.69J$
Work Step by Step
Given that engine 1 has efficiency $ e_{1}=0.18 $
suppose Amount of work done by engine 1 $=W_1$
Heat requirement of engine 1 is $=Q_1=5500J$
from definition of efficiency of engine $e_1=\frac{W_1}{Q_1}$
So $W_1=e_{1}Q_{1}$
$W_1=0.18\times5500J$
so work done by engine 1 is
$W_1=990J$.......equation(1)
Efficiency of engine 2 is $e_{2}=0.26$
given that Engine 2 dose the same work as engine 1
so work done by engine 2 is $W_2=W_1=990J$
suppose it requires heat $Q_1$
from definition of efficiency of engine $e_2=\frac{W_2}{Q_2}$
$Q_2=\frac{W_2}{e_2}$
$Q_2=\frac{990J}{0.26}$
$Q_2=3807.69J$
