Question

Two rods of the same material, same length and same radius transfer a given amount of heat in t second when they are joined end-to-end. When the rods are joined one above the other, then they will transfer the same heat in the same conditions in time ______.

पर्याय

• `t/2s`

• `t/8s`

• 2t s

• t s

Answer 1

Two rods of the same material, same length and same radius transfer a given amount of heat in t second when they are joined end-to-end. When the rods are joined one above the other, then they will transfer the same heat in the same conditions in time `underlinebb(t/8s)`.

Explanation:

Since, heat transfer, Q = `(KA(T_1 - T_2) xx t)/L`

The equivalent thermal resistance in series i.e. joined end-to-end is,

`1/K_{eq} = 1/K_1 + 1/K_2 = 1/K + 1/K`

⇒ `1/K_{eq} = 2/K ⇒ K_{eq} = K/2`

The equivalent thermal resistance in parallel i.e. when they are joined one above another,

`K_{eq} = K_1 + K_2 = K + K = 2K`

According to the question,

`Q_2 = Q_1`

⇒ `(2Kt_2)/L = ((K"/"2)t_1)/(2L) ⇒ t_2 = t_1/8 = t/8 s` [∴ t₁ = t]