a rod has negligible heat capacity has length 20 cm area 1 cm2 & thermal conductivity 200 . the temp at one endis 0degree and the other end is slowly and linearly varied from 0--60degree . assuming no loss of heat find total heat transmitted

dQ/dt=kA*60/(length) Watt

Lets consider the temperature difference to be a function of time then T=kt (k is a arbitary constant)

Then heat current at any time t = dQ/dt= KA (T)/l => dQ/dt = KA (kt)/l

Q= ∫KA (kt)/l.dt= KA (kt²)/2l

Since T=kt then t= T/k

Q= KA(T²)/2kl

So k(the rate at which temperature is varied with time) shold be specified for solution