Question

A 500-mL bottle of water at room temperature and a 2-L bottle of water at the same temperature were placed in a refrigerator. After 30 minutes, the 500-mL bottle of water had cooled to the temperature of the refrigerator. An hour later, the 2-L of water had cooled to the same temperature. When asked which sample of water lost the most heat, one student replied that both bottles lost the same amount of heat because they started at the same temperature and finished at the same temperature. A second student thought that the 2-L bottle of water lost more heat because there was more water. A third student believed that the 500-mL bottle of water lost more heat because it cooled more quickly. A fourth student thought that it was not possible to tell because we do not know the initial temperature and the final temperature of the water. Indicate which of these answers is correct and describe the error in each of the other answers.

Short answer

The bottle of water containing 2L of water would lose more heat.

The explanation given by the second student is the most appropriate.

Step-by-step solution

Given information

The heat required to raise the temperature of a substance is given by the formula Q = C \( \times \)m\( \times \)\(\Delta \)T,where “C” is the specific heat of the substance, “m” is the mass of the substance, and “∆T” is the change in the temperature of the substance.

Explanation by the first student

Since both the bottles contain water, the specific capacity of the water would be the same, which is 4.186 \(\frac{J}{{{g^0}C}}\).

The change in temperatures in both cases is also the same.

But the mass of the water is different. So the heat loss would be different in both cases. Therefore, the explanation given by the first student is incorrect.

A 2-L bottle of water loses more heat because there is more water. So, the explanation given by the second student is correct.

Explanation by the third student

The mass of the water is greater for a bottle containing 2L of water. Since the mass of water is density times volume, the greater the volume, the greater its mass.

So, the explanation given by the third student is also incorrect.

Explanation by the fourth student

The initial temperature is room temperature, and the final temperature is the refrigerator’s temperature. Since both the bottles are at the same temperature, the change in temperature in both cases is the same.

So, the explanation given by the fourth student is also incorrect.