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A rod of negligible heat capacity has length 40 cm, area of cross-section 1.0 cm^2 and thermal conductivity 100 W/m-°C. The temperature of one end is maintained at 0°C and that of the other end is slowly and linearly varied from (1°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 (in J).ANS IS: 450 joules

A rod of negligible heat capacity has length 40 cm, area of cross-section 1.0 cm^2 and thermal conductivity 100 W/m-°C. The temperature of one end is maintained at 0°C and that of the other end is slowly and linearly varied from (1°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 (in J).ANS IS: 450 joules

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1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
The temperature of the other end of the rod varies asT=(\dfrac{60-1}{10\times 60})t

Hence the rate of transfer of heat at any point t is

\dfrac{dH}{dt}=\dfrac{KA}{l}(T-0) =\dfrac{100\times 10^{-4}}{0.4}(\dfrac{59}{600})t

Hence the total amount of heat transfered can be found out by integrating both sides with respect totfrom 0s to 600s.

HenceH=450J

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