Question

If you add boiling water to a cup at room temperature, what would you expect the final equilibrium temperature of the unit to be? You will need to include the surroundings as part of the system. Consider the zeroth law of thermodynamics.

Short answer

The final equilibrium temperature of the unit or the system will be the same as the room temperature. The heat flow of a system is from higher to lower. Here the heat is the transfer from the hot water to the surroundings until it attains the same temperature.

Step-by-step solution

The zeroth law of thermodynamics

The law states that when two objects with different temperatures are in thermal contact with each other. And the heat will flow from the hot object to the cold one until the temperature of both objects will same.

Heat transfer to the surroundings

Here you are adding boiling water to a cup that is at room temperature. The surrounding temperature is less than the temperature of the water. So, the heat energy transfer from hot water to the surrounding air, so that they reach thermal equilibrium with each other if you placed it for some time.