Two bodies at unequal temperatures are mixed inside a calorimeter....

A calorimeter acts as an isolated system where no heat exchange takes place with the surroundings.

According to the first law of thermodynamics, $\Delta Q = \Delta U + \Delta W$.

Since the system is isolated, the net heat exchange with the surroundings is zero ($\Delta Q = 0$) and no external work is done ($\Delta W = 0$).

Therefore, the change in the total internal energy of the system is zero ($\Delta U = 0$).

This implies that the total internal energy of the two bodies remains conserved during the mixing process, even though heat flows from the hotter body to the colder body.