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 is placed together with a uniform 3 kg block of iron at an initial temperature of 20 degree Celsius. What is the temperature of the two blocks at thermal equilibrium?
Given: specific heat capacity of copper = 380 J/kg*K, specific heat capacity of iron = 450 J/kg*K
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.