A rod of negligible heat capacity has a length of 50 cm, area of cross section `5cm^(2)` and thermal conductivity 500 `W//m^(@)C`. The temperature of one end is maintained at `0^(@)C` and that fo the other end is slowly and linearly varied from `0^(@)C` to `60^(@)C` in 20 min. Assuming no heat loss through the lateral side, the total heat transmitted throught he rod in 20 minutes is

Options

A. 18 kJ
B. 8 kJ
C. 27 kJ
D. 4.5 kJ

Answer

A

Explanation

`T=(t)/(20) .^(@)C` where t is time is seconds
`(d theta)/(dt)=(kA(T-0))/(l)`
`DeltaQ=intdQ=(kA)/(l)int(t)/(20)dt=18000J`.