Question

A rod of negligible heat capacity has length 20cm, area of cross section `1.0cm^(2)` and thermal conductivity `200Wm^(-1)`^(@)C^(-1)` . The temperature of one end is maintained at `0^(@)C` and that of the other end is showly and linearly varied from `0^(@)C` to `60^(@)C` in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these 10 minutes.

Answer 1

Correct Answer - A
`(d theta)/(dt)= 60/(10xx60)=0.10^(@)C//sec`
`(d theta)/(dt)=(KA)/d(theta_1-theta_2)`
`=(KA0.1)/d+(KA0.2)/d+….+(KA60)/d` ltbrge(KA)/d(0.1+0.2+….+60)`
`(KA)/d (600/2) (2xx0.1+599xx0.1)`
`[a+2a+…na=(n)/(2){2a+(n-1)a}]`
`=(200xx1xx10^(-4))/(20xx10^(-2))xx300xx(0.2+59.9)`
`=(200xx10^(-2)xx300(60.1))/20`
`=3xx10xx60.1`
`=1803W=1800W.`