Question

The two ends of a rod of length $$L$$ and a uniform cross-sectional area $$A$$ are kept at two temperatures $${T_1}$$ and $${T_2}\left( {{T_1} > {T_2}} \right).$$   The rate of heat transfer, $$\frac{{dQ}}{{dt}},$$  through the rod in a steady state is given by

A. $$\frac{{dQ}}{{dt}} = \frac{{KL\left( {{T_1} - {T_2}} \right)}}{A}$$
B. $$\frac{{dQ}}{{dt}} = \frac{{K\left( {{T_1} - {T_2}} \right)}}{{LA}}$$
C. $$\frac{{dQ}}{{dt}} = KLA\left( {{T_1} - {T_2}} \right)$$
D. $$\frac{{dQ}}{{dt}} = \frac{{KA\left( {{T_1} - {T_2}} \right)}}{L}$$  
Answer :   $$\frac{{dQ}}{{dt}} = \frac{{KA\left( {{T_1} - {T_2}} \right)}}{L}$$
Solution :
For a rod of length $$L$$ and area of cross-section $$A$$ whose faces are maintained at temperatures $${T_1}$$ and $${T_2}$$ respectively.
Then in steady state the rate of heat flowing from one face to the other face in time $$t$$ is given by $$\frac{{dQ}}{{dt}} = \frac{{KA\left( {{T_1} - {T_2}} \right)}}{L}$$

Releted MCQ Question on
Heat and Thermodynamics >> Conduction

Releted Question 1

A wall has two layers $$A$$ and $$B,$$ each made of different material. Both the layers have the same thickness. The thermal conductivity of the meterial of $$A$$ is twice that of $$B.$$ Under thermal equilibrium, the temperature difference across the wall is $${36^ \circ }C.$$  The temperature difference across the layer $$A$$ is

A. $${6^ \circ }C$$
B. $${12^ \circ }C$$
C. $${18^ \circ }C$$
D. $${24^ \circ }C$$
View Answer
Releted Question 2

Three rods of identical cross - sectional area and made from the same metal from the sides of an isosceles triangle $$ABC,$$  right - angled at $$B.$$ The points $$A$$ and $$B$$ are maintained at temperatures $$T$$ and $$\left( {\sqrt 2 } \right)$$  $$T$$ respectively. In the steady state, the temperature of the point $$C$$ is $${T_c}.$$  Assuming that only heat conduction takes place, $$\frac{{{T_c}}}{T}$$ is

A. $$\frac{1}{{2\left( {\sqrt 2 - 1} \right)}}$$
B. $$\frac{3}{{\sqrt 2 + 1}}$$
C. $$\frac{1}{{\sqrt 3 \left( {\sqrt 2 - 1} \right)}}$$
D. $$\frac{1}{{\sqrt 2 + 1}}$$
View Answer
Releted Question 3

Three rods made of same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $${0^ \circ }C$$  and $${90^ \circ }C$$  respectively. The temperature of the junction of the three rods will be
Conduction mcq question image

A. $${45^ \circ }C$$
B. $${60^ \circ }C$$
C. $${30^ \circ }C$$
D. $${20^ \circ }C$$
View Answer
Releted Question 4

Two identical rods are connected between two containers one of them is at $${100^ \circ }C$$  and another is at $${0^ \circ }C.$$  If rods are connected in parallel then the rate of melting of ice is $${q_1}\,gm/sec.$$   If they are connected in series then the rate is $${{q_2}}.$$ The ratio $$\frac{{{q_2}}}{{{q_1}}}$$ is

A. 2
B. 4
C. $$\frac{1}{2}$$
D. $$\frac{1}{4}$$
View Answer

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Conduction

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