A cooking pan whose inner diameter is 20 cm is filled with water and covered with a 4-kg lid. I

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A cooking pan whose inner diameter is 20 cm is filled with...

A cooking pan whose inner diameter is $20 \mathrm{~cm}$ is filled with water and covered with a $4-\mathrm{kg}$ lid. If the local atmospheric pressure is $101 \mathrm{kPa}$, determine the temperature at which the water starts boiling when it is heated.

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the air in the Earth's atmosphere. It plays a crucial role in determining phase changes such as boiling, because a liquid boils when its vapor pressure equals the external pressure, which includes atmospheric pressure and any additional pressure applied over the liquid's surface.

Pressure from Additional Load

When an extra weight or load is applied to the surface of a liquid, it increases the pressure on the liquid beyond the ambient atmospheric pressure. This additional pressure is calculated by dividing the force due to the weight by the area over which it is applied, and it directly affects the temperature at which the liquid will boil by requiring a higher vapor pressure to overcome the total pressure.

Vapor Pressure

Vapor pressure is the pressure exerted by the vapor in equilibrium with its liquid phase at a given temperature. It increases with temperature, and boiling begins when this vapor pressure equals the total external pressure acting on the liquid's surface.

Boiling Point and Vapor Pressure Equilibrium

The boiling point of a liquid is defined as the temperature at which its vapor pressure becomes equal to the external pressure surrounding it. Thus, when additional external pressure is applied (for instance, from atmospheric conditions or an extra load on a container), the liquid must reach a higher temperature to achieve the same vapor pressure for boiling to occur.

Clausius-Clapeyron Relation

The Clausius-Clapeyron equation describes the quantitative relationship between the vapor pressure of a liquid and its temperature. It is used to determine how the boiling point changes with varying external pressures, providing insight into phase equilibrium and the energy involved in phase transitions.

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