Let's break down the question shown in the image: **Question:** > Consider a room filled with air at 15°C and 75% relative humidity. Calculate the temperature of the windows of the room at which air starts condensing at the inner surface. This is asking for the **dew point temperature**—the temperature at which condensation begins. ### Step-by-Step Solution 1. **Given Data:** - Air temperature (T) = **15°C** - Relative Humidity (RH) = **75%** 2. **Find the Dew Point (Td):** The dew point can be estimated using the following formula: \[ Td = T - \left(\frac{100 - RH}{5}\right) \] Plug in the values: \[ Td = 15 - \left(\frac{100 - 75}{5}\right) \] \[ Td = 15 - \left(\frac{25}{5}\right) \] \[ Td = 15 - 5 = 10°C \] ### Check the Options From the image, the options are: - 12.7°C - 9°C - 10.8°C - 9.3°C The closest value to our calculation is **10.8°C**. ### More Accurate Calculation (for completeness) Using the **Magnus formula** for dew point: \[ Td = \frac{b \cdot \alpha(T, RH)}{a - \alpha(T, RH)} \] where \[ \alpha(T, RH) = \frac{aT}{b+T} + \ln\left(\frac{RH}{100}\right) \] Typical values: \(a=17.27\), \(b=237.7°C\). \[ \alpha = \frac{17.27 \times 15}{237.7 + 15} + \ln(0.75) \] \[ = \frac{259.05}{252.7} + (-0.2877) \] \[ = 1.025 + (-0.2877) = 0.7373 \] \[ Td = \frac{237.7 \times 0.7373}{17.27 - 0.7373} \] \[ = \frac{175.17}{16.5327} \] \[ = 10.6°C \] This value is closest to **10.8°C**. --- ## **Final Answer:** **10.8°C** That's the temperature at which the air starts condensing on the window's inner surface.