Question

Two pieces of copper and aluminium of equal thickness and equal cross sectional are joint together one end of copper is kept at 100°c and the other end of the aluminium is kept at 0 °c find the temperature at the interspace of copper and aluminium given that thermal conductivity of copper is 385 w m-1 k???? thay of the aluminium 180wmsk-1

Answer 1

Given :

Thermal conductivity of copper , K$_{copper}$ = 385  watts per kelvin

Thermal conductivity of aluminium , K$_{aluminium\\}$ = 180 watts per kelvin

Temperature at copper end = 100° C

Temperature at aluminium end = 0° C

To find :

The temperature at the junction of the rods .

Solution :

Let the length and the area of both the rods be Le and Ar , respectively.

Also let the temperature at the junction be X .

As the two rods are connected in series , the rate of heat flow through the rods should equal i.e.  Q$_{copper}$ = Q$_{aluminium}$

∴ [ K$_{copper}$ * Ar * ( 100 - X ) ] / Le =  [ K$_{aluminium\\}$  * Ar * ( X - 0 ) ] / Le

=>  K$_{copper}$ *  ( 100 - X ) = K$_{aluminium\\}$   * ( X - 0 )

=> 385 * ( 100 - X ) = 180 X

=> 565 X = 38500

=> X = 68.14 ° C

The temperature at the junction of the two rods is 68.14 ° C