## 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 isit's specific heat capacity isand it's initial temperature isthen the stored heat isWhen it comes into contact with a cooler body of massspecific heat capacityand initial temperaturewith stored heat energythe temperature of the hotter one decreases toand and it's stored heat energy falls toThe temperature of the cooler one increases toand 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. Sinceand 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