Question 65

The Correct Answer is C ### Explanation for C ($59.0^{\circ}F$) The dew point ($T_{dp}$) is the temperature at which water vapor begins to condense. It is determined by the specific humidity of the air, which can be calculated using the dry bulb temperature ($T_{db}$) and wet bulb temperature ($T_{wb}$). Given: * Dry Bulb Temperature ($T_{db}$) = $78.0^{\circ}F$ * Wet Bulb Temperature ($T_{wb}$) = $66.5^{\circ}F$ The relationship between these variables is typically determined using a psychrometric chart or specialized psychrometric equations (like the one derived from the Carrier equation). 1. **Calculate the Wet Bulb Depression ($\Delta T$):** $$\Delta T = T_{db} - T_{wb} = 78.0^{\circ}F - 66.5^{\circ}F = 11.5^{\circ}F$$ 2. **Determine Relative Humidity (RH):** Using a psychrometric calculator or chart for $T_{db} = 78^{\circ}F$ and $T_{wb} = 66.5^{\circ}F$, the relative humidity (RH) is found to be approximately $\mathbf{59\%}$. 3. **Calculate Dew Point ($T_{dp}$):** The dew point is the saturation temperature corresponding to this specific humidity level. Using the formula that relates $T_{db}$ and RH to $T_{dp}$ (or reading directly from the chart): $$T_{dp} \approx 59.0^{\circ}F$$ When $T_{db} = 78.0^{\circ}F$ and RH $\approx 59\%$, the air must be cooled to $59.0^{\circ}F$ for condensation to begin. Therefore, $59.0^{\circ}F$ is the correct dew point. ### Why Other Options Are Incorrect **A) $47.0^{\circ}F$:** This temperature is too low. A dew point of $47.0^{\circ}F$ would correspond to a relative humidity of about $35\%$ at $78^{\circ}F$. Since the wet bulb depression is only $11.5^{\circ}F$, the air is much wetter than $35\%$ RH. **B) $51.5^{\circ}F$:** This temperature is also too low. A dew point of $51.5^{\circ}F$ would correspond to a relative humidity of approximately $45\%$ at $78^{\circ}F$. This humidity level is still significantly lower than what is indicated by the small wet bulb depression ($11.5^{\circ}F$). **D) $70.0^{\circ}F$:** This temperature is too high. The dew point must be less than or equal to the wet bulb temperature, and the wet bulb temperature is $66.5^{\circ}F$. If the dew point were $70.0^{\circ}F$, the wet bulb temperature would also have to be $70.0^{\circ}F$ (implying $100\%$ RH), which contradicts the given wet bulb reading of $66.5^{\circ}F$.