Consider two rods of same length and different specific heats (S_… - Vidyadip

MCQ

Consider two rods of same length and different specific heats $\left(S_{1}, S_{2}\right)$, conductivities $\left(K_{1}, K_{2}\right)$ and area of cross-sections $\left(A_{1}, A_{2}\right)$ and both having temperatures $T_{1}$ and $T_{2}$ at their ends. If rate of loss of heat due to conduction is equal, then

A
${K_1}{A_2} = {K_2}{A_1}$
✓
${K_1}{A_1} = {K_2}{A_2}$
C
${K_1} = {K_2}$
D
${K_1}A_1^2 = {K_2}A_2^2$

✓

Answer

Correct option: B.

${K_1}{A_1} = {K_2}{A_2}$

b
(b) ${\left( {\frac{Q}{t}} \right)_1} = \frac{{{K_1}{A_1}({\theta _1} - {\theta _2})}}{l}$ and ${\left( {\frac{Q}{t}} \right)_2} = \frac{{{K_2}{A_2}({\theta _1} - {\theta _2})}}{l}$

given ${\left( {\frac{Q}{t}} \right)_1} = {\left( {\frac{Q}{t}} \right)_2}$

==> ${K_1}{A_1} = {K_2}{A_2}$

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