Question

Wires A and B have identical lengths and have circular cross-sections. The radius of A is twice the radius of B i.e. R_A = 2R_B . For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by –

• A. K_A = 4 K_B
• B. K_A = 2 K_B
• C. K_A= K_B/2
• D. K_A = K_B /4

Answer 1

Answer: (D)

K_A = K_B /4

Answer 2

t₁ = $\frac{K_{A}\pi(2R_{B})^{2}(T_{1}–T_{2})}{L}$t₂ = $\frac{K_{B}\pi R_{B}^{2}(T_{1}–T_{2})}{L}$

\ t₁ = t₂

K_B = 4 K_A