A composite rod is formed by joining two different materials A and B in series. Rod A has a length of 16 cm and thermal conductivity 200 W m ⁻¹ K ⁻¹ . Rod B has a length of 12 cm and thermal conductivity 100 W m ⁻¹ K ⁻¹ . Both rods have the same uniform cross-sectional area of 4 cm ^2 . The free end of rod A is kept in a steam bath at 100^ C while the free end of rod B is kept in an ice bath at 0^ C . Assuming no hea

Step-by-step solution

The thermal resistance of a rod is given by R = L KA . For rod A: L_A = 16 cm = 0.16 m K_A = 200 W m ⁻¹ K ⁻¹ A = 4 cm ^2 = 4 10⁻⁴ m ^2 R_A = 0.16 200 4 10⁻⁴ = 0.16 0.08 = 2 K W ⁻¹ For rod B: L_B = 12 cm = 0.12 m K_B = 100 W m ⁻¹ K ⁻¹ R_B = 0.12 100 4 10⁻⁴ = 0.12 0.04 = 3 K W ⁻¹ Since the rods are in series, the equivalent thermal resistance is: R_ eq = R_A + R_B = 2 + 3 = 5 K W ⁻¹ The steady heat current H is: H = T R_ eq = 100 - 0 5 = 20 W The total heat transferred in t = 168 s is: Q = H t = 20 168 = 3360 J Let m