Thermal physics

Question

If one end of a solid copper pipe with a diameter of 10 cm is kept at 100 degrees centigrade, and the other side is kept at 0 degrees centigrade, how long will it take for 1000 Joules of energy to travel along the 50 cm long pipe? The thermal conductivity is 385 W/mK.

Answer 1

The steady state solution is that the rate of heat flow will be -kAdT/dx or -kA(T(.5 m)-T(0m))/.5 m

A = π(.1m)²/4 Plug in and find the rate of heat flow in J/s

Now divide 1000 J by the rate to get the time in seconds.