Question

A uniform rod of copper $50cm$ in length is insulated on the sides. It has its ends exposed to ice and steam respectively. If there is a layer of water $1mm$ thick at each end, calculate the temperature gradient in the bar :

(Given $K$ of copper $=436W{m}^{-1}{C}^{-1}$ and $K$ of water is $0.436W{m}^{-1}{C}^{-1}$)

• A. ${30}^{o}C{m}^{-1}$
• B. ${40}^{o}C{m}^{-1}$
• C. ${50}^{o}C{m}^{-1}$
• D. ${60}^{o}C{m}^{-1}$

Answer 1

Answer: (B)

${40}^{o}C{m}^{-1}$

Consider a compound rod (water + copper + water)
$Q=\frac{0.436A(100-{\theta }_1)}{1\times {10}^3}=\frac{436A({\theta }_1-{\theta }_2)}{0.5}=\frac{0.436A({\theta }_2-0)}{1\times {10}^3}$
water copper water
Solving ${\theta }_1={60}^{\circ }C;{\theta }_2={40}^{\circ }C$
Temperature gradient $=\frac{60-40}{0.5}$
$={40}^{0}C{m}^{-1}$