A highly conducting solid cylinder of radius a and length l is surrounded by a co-axial layer of a material having thermal conductivity K and negligible heat capacity. Temperature of surrounding space (outside the layer) is $T_0,$ which is higher than the temperature of the cylinder. If heat capacity per unit volume of the cylinder material is S and outer radius of the cylinder is b, time required to increase the temperature of the cylinder from $T_{1}to{T}_2$ is (Assume end faces to be thermally insulated and given that $b=2a;T_0=500K,T_1=300K,T_2=400Kand\ln 2=0.7)\frac{S{a}^2{n}^2}{200K}$ Where n = ……..