Two conducting cylinders of equal length but | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) In the steady state,the rate of heat flow through both cylinders is the same.Let $r_1$ be the radius of the smaller cylinder and $r_2$ be the radi

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) In the steady state,the rate of heat flow through both cylinders is the same.Let $r_1$ be the radius of the smaller cylinder and $r_2$ be the radius of the larger cylinder.Given $r_2 = 2 r_1$,the cross-sectional areas are $A_1 = \pi r_1^2$ and $A_2 = \pi r_2^2 = \pi (2 r_1)^2 = 4 \pi r_1^2 = 4 A_1$.The rate of heat flow is given by $\frac{dQ}{dt} = \frac{K A \Delta T}{L}$.For the first cylinder: $\frac{dQ}{dt} = \frac{K_1 A_1 (300 - 200)}{L} = \frac{K_1 A_1 (100)}{L}$.For the second cylinder: $\frac{dQ}{dt} = \frac{K_2 A_2 (200 - 100)}{L} = \frac{K_2 (4 A_1) (100)}{L}$.Equating the two rates of heat flow:$\frac{K_1 A_1 (100)}{L} = \frac{K_2 (4 A_1) (100)}{L}$.$K_1 = 4 K_2$.Therefore,$\frac{K_1}{K_2} = 4$.

Similar Questions

In the Ingen-Hauz's experiment,the wax melts up to lengths $10 \ cm$ and $25 \ cm$ on two identical rods of different materials. The ratio of thermal conductivities of the two materials is:

The thermal conductivity of a rod is $2$. What is its thermal resistivity?

Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities $K_1, K_2, K_3, K_4$ and $K_5$. When points $A$ and $B$ are maintained at different temperatures,no heat flows through the central rod if

Vedclass Test Series

Exam Paper Generator

Online Exam Module