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 the same, which is 100°C (212°F) at sea level, as they have both reached their boiling point. (b) The vapor pressure of the water in the large container is the same as that in the small container, as they have the same temperature and vapor pressure is a function of temperature only.

Step-by-step solution

a. Comparing Water Temperature

When water is boiling, it means that it has reached its boiling point. For water, the boiling point is 100°C (212°F) at sea level (under normal atmospheric pressure). In both pans, the water is boiling, one vigorously and the other gently, but in both cases, the water has reached its boiling point. Therefore, the temperature of the water in both pans is the same, which is 100°C (212°F) at sea level.

b. Comparing Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. In this case, both containers of water are at the same temperature, which means they are in the same thermodynamic state. The vapor pressure of a liquid substance is a function of its temperature only, and not dependent on container size or the amount of liquid. Therefore, the vapor pressure of the water in the large container is the same as that in the small container, as they have the same temperature.