Chapter U3.66, Problem 6E

Interpretation Introduction

Interpretation: The relative humidity needs to be determined.

Concept Introduction:

The relative humidity is related to water vapor density as follows:

  $\text{Relative humidity}=\frac{\text{Measured water vapor density}}{\text{Maximum possible water vapor density}}\times 100\%$

Answer to Problem 6E

17.86%.

Explanation of Solution

The maximum water vapor density can be seen from the water vapor density vs. temperature graph.

  

It can be seen from the graph that the water vapor density is approximately 2.8 moles/1000L at 40 ^oC. This corresponds to 100% humidity.

The water vapor density at 40 ^oC is given 0.5 mol of water vapor per 1000 L of the air.

Thus, the relative humidity can be calculated as follows:

  $\text{Relative humidity}=\frac{\text{Measured water vapor density}}{\text{Maximum possible water vapor density}}\times 100\%$

Putting the values,

  $\begin{array}{l}\text{Relative humidity}=\frac{\text{0}\text{.5/1000 L}}{\text{2}\text{.8/1000 L}}\times 100\%\\ =17.86\%\end{array}$

Conclusion

Thus, the relative humidity is 17.86%.