Let us check the Dulong Petit law by a little experiment. We heat a known mass m=1000 g of steel to 100 Celsius by immersing it in boiling water. We then introduce the hot steel into 250 g of water held in a thermostat at room temperature.
Heat flows from the copper to the water until the temperatures have reached the same
final value:
Since atoms in copper and water to a good approximation
both have six degrees of freedom
the ratio of heat capacities is simply the ratio of moles of atoms in steel and water
The final temperature should thus be
We do the experiment and find almost perfect agreement with the calculation.
Here it should be noted that there are significant systematic
errors in this experiment coming from the finite heat capacity of the
thermostat and heat loss to the surroundings.