A uniform metallic rod conducts a steady heat current H0 when its length is L and cross-sectional area is A, the temperature difference between its ends being ΔT.
(i) Derive an expression for the new heat current H when the length is changed to mL and the area to nA, the temperature difference remaining ΔT.
(ii) Hence obtain a general formula for the percentage change in heat current in terms of the constants m and n.
(iii) Using your result, calculate the percentage change in heat current when the length is halved and the area is reduced to one-fourth of its original value.