Question

(a) Two pans of water are on different burners of a stove. One pan of water is boiling vigorously, while the other is boiling gently. What can be said about the temperature of the water in the two pans? (b) A large container of water and a small one are at the same temperature. What can be said about the relative vapor pressures of the water in the two containers?

Short answer

(a) The temperature of the water in both pans is 100°C (212°F) at sea level, regardless of whether the boiling is gentle or vigorous, as boiling occurs when the vapor pressure of the water equals the atmospheric pressure. (b) The vapor pressures of the water in the large and small containers are the same when they are at the same temperature, as vapor pressure is dependent on temperature and substance but not on volume or container size.

Step-by-step solution

Part (a) - Comparing Temperatures

To compare the temperatures of the water in the two pans, we will consider the concept of boiling. Boiling occurs when the vapor pressure of the water equals the atmospheric pressure. At this point, the water can be converted to steam, producing bubbles and the appearance of boiling. For both pans, the water is boiling, meaning that their temperatures are at the boiling point of water, which is 100°C (212°F) at sea level. This is regardless of whether the boiling is gentle or vigorous. Therefore, the temperature of the water in both pans is at 100°C (212°F) at sea level. However, it is important to note that the boiling point of water can vary depending on altitude and atmospheric pressure. The boiling point decreases with increasing altitude. Hence, it might be useful to clarify the conditions under which the comparisons are made.

Part (b) - Comparing Vapor Pressures

Given that the large container and the small one are at the same temperature, we can analyze their relative vapor pressures. Vapor pressure is the pressure exerted by the vapor when it is in equilibrium with the liquid at a given temperature. It is important to note that vapor pressure is dependent on the temperature and the substance (water, in this case), but not on the volume or container size. Since both containers have water at the same temperature, the vapor pressures of the water in the two containers will be equal. Therefore, the relative vapor pressures of the water in the large container and the small container are the same. In summary, for part (a), the temperatures of the two pans of boiling water are both at 100°C (212°F) at sea level, regardless of the boiling intensity. For part (b), the vapor pressures of the water in the large and small containers are the same when they are at the same temperature.