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