Q: Two rods A and B are of equal lengths. Their ends are kept between the same temperature and their area of cross-sections are A_{1} and A_{2} and thermal conductivities K_{1} and K_{2}. The rate of heat transmission in the two rods will be equal, if

(a) K_{1} A_{2} = K_{2} A_{1}

(b) K_{1} A_{1} = K_{2} A_{2}

(c) K_{1} = K_{2}

(d) K_{1} A_{1}^{2} = K_{2} A_{2}^{2}

Ans: (b)

Sol: Heat Current $\large i = \frac{T_1 – T_2}{R}$ …(i)

Here , R = Thermal resistance & Temperature difference is same .

As the rate of heat transmission (i) in the two rods is be equal .

⇒ $R_A = R_B$ ; from (i)

$\frac{l}{K_1 A_1} = \frac{l}{K_2 A_2} $

⇒ K_{1} A_{1} = K_{2} A_{2}