Bodies at Different Temperatures Coming to Thermal Equilibrium
When two bodies at different temperatures come into contact, heat will be transferred from one to the other until the bodies reach the same temperature. They are then said to be in thermal equilibrium. In general during this process heat energy will also be transferred to or from the surroundings. If the two bodies are isolated though, all the heat energy lost by one will be transferred to the other.
If the mass of the hotter body is
it's specific heat capacity is
and it's initial temperature is
then the stored heat is
When it comes into contact with a cooler body of mass
specific heat capacity
and initial temperature
with stored heat energy
the temperature of the hotter one decreases to
and and it's stored heat energy falls to
The temperature of the cooler one increases to
and and it's stored heat energy falls to
The change in energy of the hotter one is
The change in energy of the cooler one is
If the two bodies are isolated then these are equal in magnitude. Since
and similarly,
When in thermal equilibrium
Rearranging this gives
Example: Suppose 50kg of hot iron at a temperature of 600 ° K is dropped into 300kg of water at a temperature of 300 ° K. The specific heat capacity of iron is 460 J/kg/ ° K and of water is 4180 J/kg/ ° K. The equilibrium temperature reach assuming no heat loss to the surroundings is
