Chapter 13, Problem 63P

To determine

To Calculate:The dew point of the vapor pressure of the day using the given information.

Answer to Problem 63P

  ${14}^0\text{C}$

Explanation of Solution

Given:

Relative humidity = $50\%$

Temperature = ${25}^0\text{C}$

Calculation:

The saturated pressure is $23.8\text{torr}$ for the temperature ${25}^0\text{C}$ . According to the given situationrelative humidity is $50\%$ , then the partial pressure of water is half the saturated pressure . The temperature at which the pressure is $11.9\text{torr}$ is known as dew point .but the temperature range is from ${10}^0\text{C}$ to ${15}^0\text{C}$ . So $11.9\text{torr}$ is not calculated at this temperature. The temperature is calculated by the linear interpolation.

Temperature change per torr between $\begin{array}{l}{10}^{0}C\\ {15}^{0}C\end{array}$

  $\frac{{\left(15-10\right)}^0\text{C}}{\left(12.8-9.21\right)\text{torr}}={1.393}^0\text{C/torr}$

the temperature to $11.9\text{torr}$

  $\begin{array}{l}={10}^0\text{C}+\left[\left(11.9-9.21\right)\text{torr}\right]\left({1.393}^0\text{C/torr}\right)={13.7}^0\text{C}\approx \\ ={14}^0\text{C}\end{array}$

Conclusion:

The dew point for the vapor pressure is ${14}^0\text{C}$ .