A cylindrical metallic rod in thermal contact | vedclass

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

Question

(C) The rate of heat conduction through a rod is given by $\frac{Q}{t} = \frac{kA(T_1 - T_2)}{l}$,where $A = \pi r^2$ is the cross-sectional area and

Vedclass · Accepted Answer

$\frac{Q}{16}$

Vedclass · Answer

(C) The rate of heat conduction through a rod is given by $\frac{Q}{t} = \frac{kA(T_1 - T_2)}{l}$,where $A = \pi r^2$ is the cross-sectional area and $l$ is the length.When the rod is melted and reshaped,the volume $V = A \cdot l = \pi r^2 l$ remains constant.Let the new radius be $r' = \frac{r}{2}$.Since $V = \pi (r')^2 l' = \pi (\frac{r}{2})^2 l' = \pi \frac{r^2}{4} l'$,we have $\pi r^2 l = \pi \frac{r^2}{4} l'$,which gives the new length $l' = 4l$.The new area is $A' = \pi (r')^2 = \pi (\frac{r}{2})^2 = \frac{A}{4}$.The heat conducted by the new rod in time $t$ is $Q' = \frac{kA' (T_1 - T_2) t}{l'}$.Substituting $A' = \frac{A}{4}$ and $l' = 4l$:$Q' = \frac{k (A/4) (T_1 - T_2) t}{4l} = \frac{1}{16} \frac{kA(T_1 - T_2) t}{l}$.Since $Q = \frac{kA(T_1 - T_2) t}{l}$,we get $Q' = \frac{Q}{16}$.

Similar Questions

For a spherical shell with inner and outer radii $r_1$ and $r_2$ respectively,the formula for the heat flow rate is = ......... where $T_1$ and $T_2$ are the temperatures of the inner and outer surfaces of the shell $(T_1 > T_2)$. The thermal conductivity of the material of the shell is $k$.

The water in a lake starts freezing at a temperature of $0^{\circ}C$. If it takes $7$ hours to form $1 \ cm$ of ice when the atmospheric temperature is $-10^{\circ}C$, how much additional time will it take to increase the thickness of the ice from $1 \ cm$ to $2 \ cm$ (in $hours$)?

The lengths and radii of two rods made of the same material are in the ratios $1:2$ and $2:3$ respectively. If the temperature difference between the ends for the two rods is the same,then in the steady state,the amount of heat flowing per second through them will be in the ratio:

Three rods made of the same material and having the same cross-sectional area but different lengths $10\, cm, 20\, cm$,and $30\, cm$ are joined as shown. The temperature of the junction is ......... $^oC$.

Two metal rods $P$ and $Q$ have the same length and the same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$,and their cross-sectional areas are $A_1$ and $A_2$ respectively. If the rate of flow of heat through rod $Q$ is three times that in rod $P$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module