In a room at 21°C, 60 mL of water is poured into each of three cups. The water in cup 1 is at 15°C, the water in cup 2 is at 25°C, and the water in cup 3 is at 45°C.
b. Describe what happens to the energy present in each cup over the one-hour period and explain why.
c. Explain how equilibrium is reached in the cup.
b. Over the one-hour period, the energy present in each cup will undergo a process called thermal equilibration. This means that the heat energy will transfer between the cups until they reach a state of thermal equilibrium. In thermal equilibrium, the temperatures of the three cups will eventually equalize.
The energy transfer occurs because heat flows from a region of higher temperature to a region of lower temperature. In this case, the water in cup 2 with the highest temperature will transfer heat to the water in cup 1 and cup 3, which have lower temperatures. Conversely, the water in cup 3, with the highest temperature difference, will transfer heat to the water in cup 2 and cup 1.
During the one-hour period, the water in cup 2 will lose heat and decrease in temperature, while the water in cup 3 will lose more heat and also decrease in temperature. On the other hand, the water in cup 1 will absorb heat from both cup 2 and cup 3, causing it to increase in temperature.
c. Equilibrium is reached in a cup when the temperatures of all the cups are equal. In this scenario, equilibrium occurs when the temperatures of cup 1, cup 2, and cup 3 are all the same.
To understand how equilibrium is reached in the cup, we need to apply the concept of heat transfer. Heat always flows from a hotter body to a colder body until they both reach the same temperature. In this case, the water in cup 2 and cup 3 will lose heat to the water in cup 1 until they reach the same temperature.
The process of heat transfer occurs through conduction, convection, and radiation. Conduction involves the direct transfer of heat between substances in contact. Convection refers to the movement of heat through a fluid (in this case, the water). Radiation is the transfer of heat through electromagnetic waves.
As the water in cup 2 and cup 3 lose heat, they will transfer it to the water in cup 1 through conduction. The temperature difference between the cups will drive this heat transfer, and it will continue until all three cups reach the same temperature, which is their equilibrium temperature.
Once equilibrium is reached, there will be no further net transfer of heat between the cups. The temperature of the water in all three cups will be the same, and the energy present in each cup will no longer change.