A composite rod is made by joining two sections in series. The first section has a thermal conductivity 3K₀ , length L , and cross-sectional area A . The second section has a thermal conductivity K₀ , length L , and cross-sectional area A . The free end of the first section is placed in steam at 100^ C and the free end of the second section is placed in melting ice at 0^ C . In the steady state, what is the expressio

Step-by-step solution

Let the temperature of the junction in steady state be T . The rate of heat flow through both sections must be equal: H = 3K₀ A (100^ C - T) L = K₀ A (T - 0^ C ) L 300 - 3T = T 4T = 300 T = 75^ C The steady heat current is: H = K₀ A (75 - 0) L = 75 K₀ A L Alternatively, the equivalent thermal resistance is R_ eq = L 3K₀ A + L K₀ A = 4L 3K₀ A . The heat current is H = T R_ eq = 100 4L 3K₀ A = 75 K₀ A L . The heat reaching the ice is used to melt it. If dm dt is the mass of ice melted per unit time, then: H = dm dt L