Final answer:
As hot lava cools, its thermal energy is transferred to the surroundings through radiation, conduction, and convection. This transfer causes the molecules within the lava to lose energy and the lava's temperature to decrease until it reaches a balance with the environmental temperature.
Step-by-step explanation:
When hot lava cools, the energy of the molecules decreases. This process occurs because the thermal energy contained within the lava is transferred to the cooler surroundings. The transfer of heat can occur through radiation, conduction, and convection. Initially, the surface of the lava, being at a higher temperature than the surroundings, will predominantly lose heat by radiation. As the lava's temperature approaches the surrounding temperature, conduction and convection become more significant mechanisms for heat transfer.
The rate of energy transfer by radiation is given by the Stefan-Boltzmann law and depends on the temperature difference between the lava and the surroundings, the surface area, and the emissivity of the lava. On the other hand, heat conduction depends on the temperature gradient between the interior and the surface of the lava, the thermal conductivity of the material, and the thickness of the lava layer through which the heat is conducted.
In the case of the Kilauea volcano in Hawaii, the rate of heat transfer by convection as the lava cools down could be calculated considering the specific heat of the lava, the density, and the level of cooling from the initial temperature to the final temperature it reaches.