A copper rod is joined to a steel rod in series. The rods have equal length and equal cross – sectional area. The free end of copper rod is kept at 10°C and that of steel rod is kept at 100°C. If the thermal conductivity of copper is eight times that of steel, what is the temperature at the junction of the rods ?

Figure shows a paddle wheel coupled with an agitator submerged in a water tank placed in an ice bath. The thickness of tank walls is 2mm and with thermal conductivity $0.5\mathrm{W}/{\mathrm{m}}^{\circ }\mathrm{C}$. The surface area of tank in contact with water is $0.05{\mathrm{m}}^2$. As the block of mass M attached to wheel goes down agitator rotates. It is found that in steady state block goes down at a constant speed of 0.1m/s and water temperature remain constant at 1°C. Find the mass of block (in kg). $\text{ (Take }\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2\text{ ) }$