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Olympiad workbook

Exam: Olympiad workbook
Subject: NSEP
Chapter: Thermal Properties of Matter

Olympiad workbook · NSEP · Thermal Properties of Matter

A certain rod of uniform area of cross section A (A=1.0 ~cm^2) with...

A certain rod of uniform area of cross section

\mathrm{A}

\left(\mathrm{A}=1.0 \mathrm{~cm}^2\right)

with its length

=2 \mathrm{~m}

is thermally insulated on its lateral surface. The thermal conductivity

(K)

of the material of the rod varies with temperature

T

as K=\frac{\alpha}{T} where

\alpha

is a constant. The two ends of the rod are maintained at temperature of

T_1=90^{\circ}

. and

T_2=10^{\circ} \ldots The correct option(s) is /are

Options

AThe temperature at 50 cm from the colder end is $17.32^{{}^{{}^{\circ}}}$
BThe temperature at 50 cm from the hotter end is $51.96^{{}^{{}^{\circ}}}$
CThe rate of heat flow per unit area of cross section of the rod is $1.1 \alpha$ in SI units.
DThe temperature gradient is numerically higher near the hot end compare to that near the cold end.

Correct answer

D. The temperature gradient is numerically higher near the hot end compare to that near the cold end.

Step-by-step solution

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