Heat Transport in humidity control

Question

PROBLEM 6.11 A humidity box for laboratory use is constructed from panes of window glass of thickness 4 mm. The temperature inside the box is maintained at 90°C and the ambient room temperature is 25℃·The heat transfer coefficients at the inner and outer surfaces of the box are, respectively, 20 and 60 W.m-2.K

(a) Calculate the maximum relative humidity that can be used in the box without condensation occurring on the inner surfaces.

I know the relative humidity is the amount of water vapour pressure in air as % needed for saturation at the same temp.

What needs to be true for condensation to not occur on the inner surfaces? Would condensation not occur given any difference of temperature?

Answer 1

You need to determine the temperature at the inner surface of the window. This will tell you the saturation vapor pressure at this surface. The relative humidity allowed for the air in the box (without condensation occurring on the window) will be the saturation vapor pressure at this wall temperature divided by the saturation vapor pressure at 90 C.