Three rods each of length l and cross-section | vedclass

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

Question

(A) In a series combination of heat conductors,the rate of heat flow $(H)$ remains constant through each rod.$H = \frac{dQ}{dt} = \frac{kA(T_{high} -

Vedclass · Accepted Answer

$\frac{600}{7} {}^{\circ}C, \frac{400}{7} {}^{\circ}C$

Vedclass · Answer

(A) In a series combination of heat conductors,the rate of heat flow $(H)$ remains constant through each rod.$H = \frac{dQ}{dt} = \frac{kA(T_{high} - T_{low})}{l}$Since $A$ and $l$ are the same for all three rods,the heat current $H$ is proportional to $k \Delta T$.Let $H$ be the steady heat current. Then:$H = \frac{(2K)A(100 - T_1)}{l} = \frac{KA(T_1 - T_2)}{l} = \frac{(K/2)A(T_2 - 0)}{l}$Canceling $\frac{KA}{l}$ from all parts:$2(100 - T_1) = (T_1 - T_2) = 0.5 T_2$From the second and third parts:$T_1 - T_2 = 0.5 T_2 \Rightarrow T_1 = 1.5 T_2 = \frac{3}{2} T_2$From the first and second parts:$2(100 - T_1) = T_1 - T_2$$200 - 2T_1 = T_1 - T_2$$200 = 3T_1 - T_2$Substitute $T_1 = \frac{3}{2} T_2$ into the equation:$200 = 3(\frac{3}{2} T_2) - T_2$$200 = \frac{9}{2} T_2 - T_2 = \frac{7}{2} T_2$$T_2 = \frac{400}{7} {}^{\circ}C$Now,find $T_1$:$T_1 = \frac{3}{2} (\frac{400}{7}) = \frac{600}{7} {}^{\circ}C$Thus,the temperatures are $T_1 = \frac{600}{7} {}^{\circ}C$ and $T_2 = \frac{400}{7} {}^{\circ}C$.

Similar Questions

Two identical containers are filled with the same amount of ice. The containers are made of different metals. If the ice in both containers melts in $20$ minutes and $35$ minutes respectively,find the ratio of their thermal conductivities.

$1.56 \times 10^5 \ J$ of heat is conducted through a $2 \ m^2$ wall of $12 \ cm$ thickness in one hour. The temperature difference between the two sides of the wall is $20^{\circ} C$. The thermal conductivity of the material of the wall is (in $W \ m^{-1} \ K^{-1}$):

The two ends of a rod of length $x$ and uniform cross-sectional area $A$ are kept at temperatures $T_1$ and $T_2$ respectively $(T_1 > T_2)$. If the rate of heat transfer through the rod in steady state is $Q/t$,then the coefficient of thermal conductivity $K$ is:

Copper and iron rods of identical dimensions are coated with wax. The ratio of thermal conductivity of copper to iron is $10:9$. If one end of each rod is placed in hot water,the wax melts. Find the ratio of the lengths of the rods for which the wax melts at the same rate.

Vedclass Test Series

Exam Paper Generator

Online Exam Module