Question

2 pieces of copper and aluminum of equal thickness & cross sectional area are joined together the other end of copper is kept at 100°c & aluminium at 0°c. find the temperature junction if the thermal conductivity of copper & aluminium are 385 watt per metre kelvin & 180 watt per metre kelvin​

Answer 1

Explanation:

two rods of Copper and brass having same length and cross section are joined end to end

Answer 2

Given :

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

Thermal conductivity of aluminium , K$_{al}$ = 180 watt per kelvin

Temperature of copper end = 100° C

Temperature of aluminium end = 0° C

To find :

Temperature at junction of the rods .

Solution :

Let the length and area of both the rods be L and A, respectively.

Also let the temperature at the junction be T.

As the two rods are connected in series with each other, thus rate of heat flow through the rods must be equal i.e.  Q$_{c}$ = Q$_{al}$

∴ [ K$_{c}$ * A * ( 100 - T ) ] / L =  [ K$_{al}$ * A * ( T - 0 ) ] / L

→  K$_{c}$ *  ( 100 - T ) = K$_{al}$  * ( T - 0 )

→ 385 * ( 100 - T ) = 180 T

→ 565 T = 38500

→ T = 68.14 ° C

Temperature at junction of the rods =  68.14 ° C