Two rods of identical dimensions (Area = A, length ℓ each) are kept as shown in figure. One end of both the rods is kept at 100°C & another end at 0°C. The rods have different thermal conductivity giv

Question

Two rods of identical dimensions (Area = A, length $ℓ$ each) are kept as shown in figure. One end of both the rods is kept at 100°C & another end at 0°C. The rods have different thermal conductivity given by $K_{1} = K_{0} (1 + \frac{x}{ℓ})$ and $K_{2} = \frac{K _{0}}{2 l n 2}$ where x is the distance from the end having 100°C temperature & $K_{0}$ is a + ve constant. Find the rate of heat flow through this combination in steady state :-

TestHub · Accepted Answer

The two rods join the same 100°C and 0°C ends, so their heat currents add.
$R_{1} = \int_{0}^{ℓ} \frac{d x}{K _{0} A ( 1 + x / ℓ )} = \frac{ℓ l n 2}{K _{0} A}$
$R_{2} = \frac{ℓ}{K _{2} A} = \frac{2 ℓ l n 2}{K _{0} A}$
$\dot{Q} = Δ T (\frac{1}{R _{1}} + \frac{1}{R _{2}})$
$\dot{Q} = 100 (\frac{K _{0} A}{ℓ l n 2} + \frac{K _{0} A}{2 ℓ l n 2})$
$\dot{Q} = \frac{150 K _{0} A}{ℓ l n 2}$
Answer A.

Physics - Heat & Thermo Question with Solution | TestHub

Options:

Doubts & Discussion