SATHEE: Thermal Properties of Matter

Thermal Properties of Matter - Result Question 31

32. Which of the following circular rods (given radius $r$ and length $l$ ), each made of the same material and whose ends are maintained at the same temperature will conduct most heat?

[2005]

(a) $r = r_{0}; l = l_{0}$

(b) $r = 2 r_{0}; l = l_{0}$

(d) $r = 2 r_{0}; l = 2 l_{0}$

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Answer:

Correct Answer: 32. (b)

Solution:

(b) From given option

(i) $r = 2 r_{0}, l = 2 l_{0}$

$∴ R = \frac{2 ℓ_{0}}{K π (2 r_{0})^{2}} = \frac{ℓ_{0}}{2 K π r_{0}^{2}}$

(ii) $r = 2 r_{0}, l = l_{0}$

$∴ R = \frac{ℓ_{0}}{K π (2 r_{0})^{2}} = \frac{ℓ_{0}}{4 K π r_{0}^{2}}$

(iii) $r = r_{0}, l = 2 l_{0}$

$∴ R = \frac{2 ℓ_{0}}{K π r_{0}^{2}} = \frac{2 ℓ_{0}}{K π r_{0}^{2}}$

(iv) $r = r_{0}, l = l_{0}$

$∴ R = \frac{ℓ_{0}}{K π r_{0}^{2}} = \frac{ℓ_{0}}{K π r_{0}^{2}}$

It is clear that for option (b) resistance is minimum, hence, heat flow will be maximum.

(i) Rate of heat flow is directly proportional to area

(ii) inversely proportional to length.

$∴$ Heat flow will be maximum when $r$ is maximum and $ℓ$ is minimum. We know that $Q = \frac{T_{H} - T_{L}}{R}$

Also, Thermal resistance $R = \frac{ℓ}{K A} = \frac{ℓ}{K π r^{2}}$

Heat flow will be maximum when thermal resistance is minimum.

Thermal Properties of Matter - Result Question 31

32. Which of the following circular rods (given radius $r$ and length $l$ ), each made of the same material and whose ends are maintained at the same temperature will conduct most heat?

Answer:

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Thermal Properties of Matter - Result Question 31

32. Which of the following circular rods (given radius r and length l ), each made of the same material and whose ends are maintained at the same temperature will conduct most heat?

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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32. Which of the following circular rods (given radius $r$ and length $l$ ), each made of the same material and whose ends are maintained at the same temperature will conduct most heat?