Question

When you step out of a shower, the temperature in the bathroom is 71°F and the relative humidity is 96%. You notice that a barely perceptible amount of water has condensed on the inside of the bathroom window. Assuming that the air immediately adjaccent to the glass has the same composition as the rest of the room air, estimate the temperature of the inside glass surface.

Answer 1

Answer: The temperature of the inside glass surface is $21.05^{o}C$ (or $69.89^{o}F$).

Explanation:

At $71^{o}F$ and 96%, we will calculate the moisture content according to the psychometric content as follows.

     Moisture content = $\frac{0.0158 kg H_{2}O}{1 kg Air} \times \frac{29 kg air/mol}{18 kg H_{2}O/mol}$

                                 = $\frac{0.0255 mol H_{2}O}{\text{mol air}}$

   Mole fraction of $H_{2}O = \frac{0.0255}{1 + 0.0255}$

                             = 0.0249

Now, partial pressure of water will be calculated as follows.

    Partial pressure of $H_{2}O$ = mole fraction of $H_{2}O$ × 1 atm

                          = 0.0249 atm

At mirror of temperature T, the partial pressure of $H_{2}O$ is equal to the saturation pressure. Therefore, the saturation pressure will be 0.0249 atm.

Hence, according to the steam tables temperature at which vapor pressure of water is $21.05^{o}C$ (or $69.89^{o}F$).