# A rod of negligible heat capacity has length 20cm, area of cross section 1.0cm^(2) and thermal conductivity 200Wm^(-1)^(@)C^(-1) . The temperatur

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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.

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(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.`