Question

An iron plate $20mm$ thick, when heat is conducted at the rate of $6\times {10}^{5}cal/min-m^2$. Coefficient of thermal conductivity for metal is $0.2cal/s-cm{-}^{\circ }C$. The difference in temperature is between two sides :

• A. ${20}^{\circ }C$
• B. ${10}^{\circ }C$
• C. ${30}^{\circ }C$
• D. ${12}^{\circ }C$

Answer 1

The correct option is B ${10}^{\circ }C$

Given,

$\frac{1}{A}\times \frac{dQ}{dt}=6\times {10}^{5}cal/min.m^2=\frac{6\times {10}^5}{60\times {10}^4}cal/s.c{m}^2$

$k=0.2cal/s.cm.°C$

$l=20mm=2cm$

$\text{We Know,}$

$\frac{dQ}{dt}=\frac{kA\Delta T}{l}$

$\frac{1}{A}\times \frac{dQ}{dt}=\frac{k\Delta T}{l}$

$1=\frac{0.2\Delta T}{2}$

$\Delta T=\frac{1}{0.1}=10°C$

Hence option $\text{B}$ is correct.