The thermal conductivity of copper is 4 times that of brass. Two rods of copper and brass having same length and cross-section are joined end to end. The free end of copper is at 0°C and the free end of brass is at 100°C. The temperature of the junction is

In a steady-state condition, the rate of heat flow through two rods joined in series must be equal. The heat conduction formula is given by Q = kA(ΔT/L), where k is thermal conductivity, A is cross-sectional area, ΔT is the temperature difference, and L is length. Let the thermal conductivity of brass be K; then copper is 4K. Given both rods have the same length (L) and area (A), and the junction temperature is T, the heat flow through copper (from 0°C to T) equals the heat flow through brass (from T to 100°C). The equation is 4K * A * (T - 0) / L = K * A * (100 - T) / L. Simplifying this leads to 4T = 100 - T, which results in 5T = 100, or T = 20°C. Thus, the junction temperature is 20°C.