Question

Arrange the following rods of same material in an increasing order of rate of flow of heat when they have equal difference of temperature between their ends
a) $l=2m,r=2cm$

b) $l=4m,r=2cm$
c) $l=2m,r=1cm$
d) $l=2m,r=4cm$

• A. a, b, c, d,
• B. c, b, a, d
• C. d, a, b, c
• D. b, c, d, a

Answer 1

Answer: (B)

c, b, a, d

Let the rate of flow of heat in a uniform rod is given by:
$H=-K\times 4\pi r^2\frac{\Delta t}{l}$
Let $-K\times 4\pi \Delta t$ be a constant $X$.
Thus,
$H=\frac{r^2}{l}X$
$H_a=\frac{2^2}{2}X=2X$
$H_b=\frac{2^2}{4}X=X$
$H_c=\frac{1^2}{2}X=0.5X$
$H_d=\frac{4^2}{2}X=8X$
Hence, increasing order is c, b, a, d.