Q56PE - College Physics (Urone)

Question

Question: What is the density of water vapor in g/m³ on a hot dry day in the desert when the temperature is 40.0ºC and the relative humidity is 6.00%?

Step-by-Step Solution

Answer

Answer

The density of water vapor is  \(3.066\,{g \mathord{\left/ {\vphantom {g {{m^3}}}} \right.} {{m^3}}}\)

Step 1: Defining how relative humidity and density of water vapor are related

The relative humidity is the ratio of vapor density to the saturation vapor density expressed in percentage. Vapor density is the density of water vapor. Relative Humidity can be mathematically expressed as;

$\mathbf{\text{Percent }}\mathbf{ }\mathbf{\text{Relative Humidity}}\mathbf{ }\mathbf{\text{ = }}\mathbf{ }\frac{\mathbf{\text{Vapor }}\mathbf{ }\mathbf{\text{Density}}}{\mathbf{\text{Saturation Vapor }}\mathbf{ }\mathbf{\text{Density}}}\mathbf{\times }\mathbf{100}\mathbf{\%}$……..(1)

Step 2: Calculation of density of water vapor

The relative humidity is given as 6.00%. Saturation vapor density corresponding to the temperature of 40.0°C is 51.1 g/m³. The expression for vapor density can be derived from the equation (1). Substituting these values in the equation will give the value of vapor density.

$$\begin{gathered} \text{Vapor } \text{Density} \text{ = } \frac{\text{Percent } \text{Relative Humidity}\times \text{Saturation Vapor } \text{Density}}{100} \\ \text{ = } \frac{6.00\times 51.1g/m^3 }{100} \\ \text{ = } 3.066 g/m^3 \end{gathered}$$

So, the vapor density is  $3.066g/m^3$