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JIPMER 2007

Exam: JIPMER
Year: 2007
Subject: Physics
Chapter: Thermal Properties of Matter

JIPMER 2007 · Physics · Thermal Properties of Matter

Which of the following circular rods, (given radius r and length l...

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?

Options

A $r=2 r_0, l=2 l_0$
B $r=2 r_0, l=l_0$
C $r=r_0, l=l_0$
D $r=r_0, l=2 l_0$

Correct answer

B. $r=2 r_0, l=l_0$

Step-by-step solution

Heat conduction through a rod is rate of change of heat

\left(\frac{\Delta Q}{\Delta t}\right)

.

\therefore H=\frac{\Delta Q}{\Delta t}=K A\left(\frac{T_1-T_2}{l}\right) \Rightarrow H \propto \frac{r^2}{l}...(i)

(a) When

\begin{aligned} r & =2 r_0, l=2 l_0 \\ H & \propto \frac{\left(2 r_0\right)^2}{2l_0} \Rightarrow H \propto \frac{2 r_0^2}{l_0}\end{aligned}

(b) When

\begin{aligned} r & =2 r_0, l=l_0 \\ H & \propto \frac{\left(2 r_0\right)^2}{ l_0} \Rightarrow H \propto \frac{4 r_0^2}{l_0}\end{aligned}

(c) When

\begin{gathered}r=r_0, l=l_0 \\ H \propto \frac{r_0^2}{l_0}\end{gathered}

(d) When

\begin{aligned} r & =r_0, l=2 l_0 \\ H & \propto \frac{r_0^2}{2 l_0}\end{aligned}

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

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