# 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

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 A1 and A2 and thermal conductivities K1 and K2. The rate of heat transmission in the two rods will be equal, if

(a) K1 A2 = K2 A1

(b) K1 A1 = K2 A2

(c) K1 = K2

(d) K1 A12 = K2 A22

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)

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

⇒ K1 A1 = K2 A2