Question

-The temperature difference between the two ends ofa bar 10 m long is 50°C and that for the other bar125 m long 75°C. Both the bars have same area ofCTOSS-section. If the rates of conduction of heat in thetwo bars are the same, find the ratio of the coefficientsof thermal conductivity of the materials of the two bars.If both the bars are of same metal, find the ratio of therates of heat conduction in them. Ans. 6:5.5:6.​

Answer 1

Answer:

Ratio of thermal conductivity of two rods when rate of heat transfer is same is 6 : 5

ratio of rate of heat transfer from two rods when thermal conductivity of two rods is same is 5 : 6

Explanation:

As we know that rate of heat transfer due to conduction mode of heat transfer is given as

$\frac{dQ}{dt} = \frac{KA}{L}(T_2 - T_1)$

now we know that two rods are of same rate of heat conduction so we have

$\frac{K_1A}{10}(50) = \frac{K_2A}{12.5}(75)$

so we have

$\frac{K_1}{K_2} = \frac{75}{12.5 \times 5}$

$\frac{K_1}{K_2} = 6 : 5$

Now if two rods are of same material then the ratio of heat transfer from two rods is given as

$\frac{\frac{dQ_1}{dt}}{\frac{dQ_2}{dt}} = \frac{\frac{50}{10}}{\frac{75}{12.5}}$

$\frac{\frac{dQ_1}{dt}}{\frac{dQ_2}{dt}} = \frac{5}{6}$

#Learn

Topic : Heat transfer due to conduction

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