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?

r = 2r_o, l = 2l_o

r = 2r_o, l = l_o

r = r_o, l = l_o

r = r_o, l = l_o

Solution

r = 2r_o, l = l_o

Heat conduction through a rod is rate of change of heat $(\frac{∆ Q}{∆ t})$

$∴ H = (\frac{∆ Q}{∆ t}) = KA (\frac{T_{1} - T_{2}}{l})$

The rate of heat H is proportional to the temperature difference (T₁ - T₂) and the area of cross section A and inversely proportional to length L. Here K is called thermal conductivity of the material.

$\Rightarrow H \propto \frac{r^{2}}{l} (a) When r = 2 r_{o}, l = 2 l_{o} H \propto \frac{{(2 r_{o})}^{2}}{l_{o}} \Rightarrow H \propto \frac{2 r_{o}^{2}}{I_{o}}$

$(b) When r = 2 r_{o}, l = l_{o} H \propto \frac{{(2 r_{o})}^{2}}{2 l_{o}} \Rightarrow H \propto \frac{4 r_{o}^{2}}{l_{o}} (c) When r = r_{o}, l = l_{o} H \propto \frac{r_{o}^{2}}{l_{o}} (d) When r = r_{o}, l = 2 l_{o} H \propto \frac{r_{o}^{2}}{2 l_{o}}$

it is obvious that heat conduction will be more in case (b).

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Thermal Properties Of Matter

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?

r = 2r_o, l = 2l_o

r = 2r_o, l = l_o

r = r_o, l = l_o

r = r_o, l = l_o

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Thermal Properties Of Matter

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? r = 2ro, l = 2lo r = 2ro, l = lo r = ro, l = lo r = ro, l = lo

Some More Questions From Thermal Properties of Matter Chapter

A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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?

r = 2r_o, l = 2l_o

r = 2r_o, l = l_o

r = r_o, l = l_o

r = r_o, l = l_o