A house wall of cross-sectional area \(A\) and thickness \(L\) is made of an insulating material with thermal conductivity \(k\). When a temperature difference \(\Delta T\) is maintained between the inner and outer surfaces of the wall, the rate of heat transfer by conduction is \(H_0\). A second identical layer of the same material and thickness \(L\) is added directly against the first wall, doubling the total thickness to \(2L\). If the same total temperature difference \(\Delta T\) is maintained across the entire two-layer wall, what is the new rate of heat transfer through the wall?