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Chapter 14: Problem 70

Explain how vapor pressure of the ambient air is determined when the temperature, total pressure, and relative humidity of the air are given.

Short Answer

Expert verified
Answer: To determine the vapor pressure of ambient air, apply the following steps: 1. Understand the concept of saturation vapor pressure, which is the pressure of water vapor in the air when it is saturated and depends on temperature. 2. Use the formula for relative humidity: Relative Humidity (RH) = (Vapor Pressure) / (Saturation Vapor Pressure) * 100 3. Calculate saturation vapor pressure using the August-Roche-Magnus equation: Saturation Vapor Pressure = 0.61094 * e^((17.625 * T) / (T + 243.04)), where T is the temperature in degrees Celsius. 4. Rearrange the RH formula to solve for vapor pressure: Vapor Pressure = (Relative Humidity / 100) * Saturation Vapor Pressure 5. Plug in the given temperature and relative humidity values into the formulas to calculate the vapor pressure of the ambient air.

Step by step solution

01

Understanding Saturation Vapor Pressure

Saturation vapor pressure is the pressure of water vapor in the air when the air is saturated, which means it can no longer hold more water vapor. The saturation vapor pressure depends on the temperature of the air, and it increases as the temperature increases.
02

Introduce the formula for Relative Humidity

Relative humidity (RH) is the ratio of the current amount of water vapor in the air (vapor pressure) to the maximum amount of water vapor the air can hold (saturation vapor pressure). The formula for relative humidity can be written as: Relative Humidity (RH) = (Vapor Pressure) / (Saturation Vapor Pressure) * 100
03

Calculate Saturation Vapor Pressure

To determine saturation vapor pressure, we can use the Clausius-Clapeyron equation or a simpler approximation known as the August-Roche-Magnus equation. We'll use the latter for this example: Saturation Vapor Pressure = 0.61094 * e^((17.625 * T) / (T + 243.04)) Where T is the temperature in degrees Celsius, and e is the base of the natural logarithm (approximately 2.718).
04

Calculate Vapor Pressure from Relative Humidity

Now that we have the formula for saturation vapor pressure, we can rearrange the RH formula to solve for vapor pressure: Vapor Pressure = (Relative Humidity / 100) * Saturation Vapor Pressure
05

Determine Vapor Pressure of Ambient Air

Plug the given temperature and relative humidity values into the formulas from Steps 3 and 4 to calculate the vapor pressure of the ambient air. For example, if the temperature is 25°C and the relative humidity is 50%, the vapor pressure would be: 1. Calculate the saturation vapor pressure: Saturation Vapor Pressure = 0.61094 * e^((17.625 * 25) / (25 + 243.04)) Saturation Vapor Pressure ≈ 3.169 kPa 2. Calculate the vapor pressure: Vapor Pressure = (50 / 100) * 3.169 Vapor Pressure ≈ 1.584 kPa Thus, the vapor pressure of the ambient air is approximately 1.584 kPa.

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