Question

Three substances are added to a mug to make coffee: coffee at ${65}^{\circ }\text{C}$, milk at ${65}^{\circ }\text{C}$ and sugar. If the sugar is in thermal equilibrium with the coffee, then which of the following is true?

• A. Heat will be transferred from sugar to milk to reach thermal equilibrium.
• B. The sugar is in themal equilibrium with the milk.
• C. Heat will be transferred from the coffee to the sugar to reach thermal equilibrium.
• D. None of these conclusions are valid.

Answer 1

The correct option is B The sugar is in themal equilibrium with the milk.

From the zeroth law of thermodynamics, we can say that, if two objects are in thermal equilibrium with a third object, then they must be in thermal equilibrium with each other.
So in our example, given the coffee and milk are in thermal equilibrium with each other (same temperature).
Also, the sugar is in thermal equilibrium with coffee.
Hence, the sugar will be in thermal equilibrium with milk.
Thus, only option (b) is the correct answer.