Can you please help me with this problem about thermal equilibrium?
It is a common experience that when we pour hot tea in a mug, the mug gets warm and we have to hold it using its handle. This is simply because heat from the tea has been transferred to the mug. Similarly, over the course of the next few minutes, the tea and the mug get cold. This happens because the mug and the tea lose heat to the colder surroundings.
This shows that heat flows from a region of higher temperature to a region of lower temperature. This rule always holds true. In the present case, the plastic cup is at 70 degrees F while the water is at 40 degrees F. The heat will flow from the hotter substance to the colder substance, which means it will flow from the plastic cup to the water (in this case). The heat transfer would be faster initially, since the temperature difference is higher between the two regions. Over time, as the water's temperature goes up and that of the cup goes down, heat transfer will slow down. In the end, both the objects will come to the same temperature. That is, the water and the cup will be in thermal equilibrium.
Among the given options, choice C is correct.
Hope this helps.