Four rods of the same material with different | vedclass

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

Question

(A) The rate of heat conduction through a rod is given by $H = \frac{K A \Delta T}{l}$,where $K$ is the thermal conductivity,$A = \pi r^2$ is the cros

Vedclass · Accepted Answer

$r = 2 \, cm, l = 0.5 \, m$

Vedclass · Answer

(A) The rate of heat conduction through a rod is given by $H = \frac{K A \Delta T}{l}$,where $K$ is the thermal conductivity,$A = \pi r^2$ is the cross-sectional area,and $l$ is the length.Since the material is the same,$K$ is constant. For a fixed temperature difference $\Delta T$,the rate of heat flow is proportional to $\frac{r^2}{l}$.Let $X = \frac{r^2}{l}$. We calculate $X$ for each option:$A: X = \frac{(2)^2}{0.5} = \frac{4}{0.5} = 8$$B: X = \frac{(2)^2}{2} = \frac{4}{2} = 2$$C: X = \frac{(0.5)^2}{0.5} = 0.5$$D: X = \frac{(1)^2}{1} = 1$Comparing the values,option $A$ has the highest value of $X$,meaning it will conduct the most heat.

Four rods of the same material with different radii $r$ and length $l$ are used to connect two reservoirs of heat at different temperatures. Which one will conduct the most heat?

Similar Questions

Four rods with different radii $r$ and length $l$ are used to connect two heat reservoirs at different temperatures. Which one will conduct the most heat?

The heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,the ratio of the rate of flow of heat through them will be:

$A$ rod of length $l$ with thermally insulated lateral surface is made of a material whose thermal conductivity $K$ varies as $K = C/T$,where $C$ is a constant. The ends are at temperatures $T_1$ and $T_2$. The heat current density is

Vedclass Test Series

Exam Paper Generator

Online Exam Module