Question

A rod of negligible heat capacity has length 20 cm, area of cross- section $1.0c{m}^2$ and thermal conductivity $200W/m^{\circ }C$. The temperature of one end is maintained at $0^{\circ }C$ and that of the other end is slowly and linearly varied from $0^{\circ }C$ to ${60}^{\circ }C$ in 10 minutes. Assuming no loss of heat through the sides find the total heat transmitted through the rod in these 10 minutes.

• A. 1800 Joule
• B. 2000 J
• C. 2200 J
• D. 2400 J

Answer 1

The correct option is A 1800 Joule

Since temperature is varying linearly so
$T=\frac{60}{10\times 60}{t}^{\circ }C/sec.={\frac{t}{10}}^{\circ }C/sec$
Now,
$\frac{dH}{dt}=\frac{dH}{dt}\frac{dH}{dt}=\frac{KAT}{l}\frac{dH}{dt}=\frac{KAt}{10l}H=\frac{KA{t}^2}{20l}=\frac{200\times 1\times {10}^{-4}\times (600{)}^2}{20\times 20\times {10}^{-2}}=1800Joule$