What is the temperature at thermal equilibrium in the following case?A uniform 3 kg block of copper at an initial temperature of 80 degree Celsius...

The specific heat capacity of copper is given as 380
J/kg*K and the specific heat capacity of iron is 450
J/kg*K.

The block made of copper is at 80 degree Celsius
and the block made of iron is at 20 degree Celsius. If the equilibrium temperature
reached after they come in contact is T, the heat gained by one should be equal to the
heat lost by the other.

When copper cools from 80 to T it
releases (80 - T)*3*380 J. When iron heats up from 20 to T it absorbs heat equal to (T -
20)*3*450 J. Now the two are equal:

=> (80 -
T)*3*380 = (T - 20)*3*450

=> (80 - T)*38 = (T -
20)*45

=> 80* 38 - 38T = 45T -
45*20

=> T*(45 + 38) = 38*80 +
45*20

=> T = 3940 /
73

=> T = 47.46 degree
Celsius.

The required temperature at thermal
equilibrium is 47.46 degree Celsius.