Question

A 50 cm long rod is half aluminum and half copper. The aluminum end is in boiling water. The end of an aluminum rod (50 cm long) is maintained at 100 C by immersing in a pot of boiling water and the other end at 00C by an ice-water mixture. If the cross-sectional area of the rod is 1.3 cm2, how much will the rod melt in 20 min? What will be the steady temperature at the Al-Cu junction?

Answer 1

Since the rod is made up of copper and aluminium, it will not melt since their melting points are not reached. Melting point of copper is 1085 degree Celsius and melting point of aluminium is around 660 degree Celsius.

The temperature of the junction at steady state-

Let T be the temperature of the interface of the two slabs and Q1 and Q2 be the rates of flow of heat through aluminium and copper respectively.

K1= coefficient of thermal conductivity of aluminium i.e. 215 W/mK approx.

t1= temperature at which aluminium part of the rod is in contact with i.e 100 degree Celsius.= 373K

x1=length of the aluminium portion of the rod i.e. 25 cm

K1= coefficient of thermal conductivity of copper i.e 369 W/mK

t1= temperature at which copper part of the rod is in contact with i.e 0 degree Celsius i.e 273 K

x1=length of the copper portion of the rod i.e. 25 cm

At steady state-

and their area of cross sections are also same.

or