Question 37: Thermodynamics & KTG

Question

The rate of heat conduction in the given two metal rods having the same length is found to be the same when the temperature difference between the ends is kept $30^{\circ} \mathrm{C}$ If the area of cross section of the first rod is $8 	imes 10^{-2} \mathrm{~m}^2$ then what will be area of cross section of the second rod? [ Given that the ratio of the thermal conductivity of the first rod to that of the second rod is $1: 4$ ]

Accepted Answer

Since for both rods
$$\frac{Q}{t}=\frac{kA\,\Delta T}{L}$$
and $L$ and $\Delta T$ are the same, equate
$$k_1A_1=k_2A_2\,. $$
With $k_1:k_2=1:4$ we get
$$A_2=\frac{k_1}{k_2}\,A_1=\frac{1}{4}	imes8	imes10^{-2}=2	imes10^{-2}	ext{ m}^2.$$
Answer: Option A.

Answer

$2 	imes 10^{-2} \mathrm{~m}^2$

Answer

$4 	imes 10^{-4} \mathrm{~m}^2$

Answer

$2 	imes 10^{-4} \mathrm{~m}^2$

Answer

$4 	imes 10^{-2} \mathrm{~m}^2$

Thermodynamics & KTG

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