A composite rod of uniform cross-section is made of two different materials A and B connected in series. The steady-state temperature distribution along the length of the rod is plotted as a graph of temperature ( T ) versus distance ( x ) from the hotter end. The graph consists of two straight line segments: the first segment for material A goes from (x=0 cm , T=100^ C ) to (x=10 cm , T=60^ C ) , and the second segm

Step-by-step solution

In steady state, the heat current H is the same through both materials. The magnitude of the temperature gradient for material A is: | dT dx |_A = 100 - 60 10 - 0 = 4^ C/cm The magnitude of the temperature gradient for material B is: | dT dx |_B = 60 - 0 30 - 10 = 60 20 = 3^ C/cm Using Fourier's law of heat conduction, H = K A | dT dx | . Equating the heat currents for the two materials in series: K_A A (4) = K_B A (3) K_A K_B = 3 4 Answer: 3 4