The Density of Water Vapor at the Boiling Point of Water

At the boiling point of water, which is 100°C (212°F) at standard atmospheric pressure, the density of water vapor is a crucial parameter for various scientific and engineering applications. At this temperature, water transitions from its liquid state to a gaseous state, creating water vapor that is less dense compared to its liquid counterpart. The density of water vapor at this temperature is approximately 0.597 kg/m³. This value is derived from the ideal gas law, which provides a good approximation under standard conditions.

To understand this in more detail, we need to consider several factors:

1. Temperature Impact: As the temperature increases, the density of water vapor decreases. This is due to the fact that higher temperatures cause water molecules to move more rapidly and occupy more space, reducing the density.

2. Pressure Consideration: The density of water vapor also varies with pressure. At the boiling point, the water vapor is at its saturation point, meaning it is in equilibrium with the liquid phase. This saturation pressure at 100°C is 101.3 kPa (1 atm). If the pressure changes, the density of the water vapor will also change accordingly.

3. Ideal Gas Law Application: The density can be calculated using the ideal gas law, which in its rearranged form to find density ($\rho$ρ) is given by:

   $\rho =\frac{P}{R\cdot T}$ρ=R⋅TP​

   where $P$P is the pressure, $R$R is the specific gas constant for water vapor (approximately 461.5 J/(kg·K)), and $T$T is the temperature in Kelvin. At 100°C (373.15 K) and 101.3 kPa, the density calculated is indeed about 0.597 kg/m³.

4. Practical Applications: Knowing the density of water vapor at boiling point is essential in fields such as meteorology, climatology, and engineering. For instance, in weather forecasting, the amount of water vapor in the air influences humidity calculations and weather predictions. In engineering, understanding the density of water vapor can aid in the design of systems that involve steam, such as turbines and boilers.

Key Takeaway: At the boiling point of water (100°C), the density of water vapor is approximately 0.597 kg/m³. This value is crucial for applications involving steam and humidity, and it is subject to changes based on temperature and pressure.