Question

A batch of material is dried under constant drying conditions. When drying is taking place from all the surfaces, the rate of drying during the constant rate period is

• A. Directly proportional to the solid thickness
• B. Inversely proportional to the solid thickness
• C. Independent of solid thickness
• D. Directly proportional to the square of solid thickness

Hint:

Imagine a wet towel drying in the wind. As long as the surface of the towel is wet, the rate at which water evaporates depends on the wind speed, air temperature, and humidity, not the thickness of the towel. The thickness will, however, affect how long the constant rate period lasts.

Answer 1

The Correct Option is C

Step 1: Understand the constant rate period of drying.
The drying process of a porous solid typically occurs in two main periods: the constant rate period and the falling rate period. During the constant rate period, the surface of the solid is so wet that a continuous film of water exists over the entire drying surface. The rate of evaporation from this surface is essentially the same as the rate of evaporation from a free water surface under the same drying conditions (air temperature, humidity, and flow rate). 
Step 2: Identify the factors affecting the rate of drying during the constant rate period.
The rate of drying during the constant rate period is primarily controlled by the external conditions and the area available for evaporation. The key factors are:
Air temperature: Higher air temperature provides more sensible heat for evaporation.
Humidity of the air: Lower humidity provides a larger vapor pressure difference, driving faster evaporation.
Air velocity over the surface: Higher air velocity increases the convective mass transfer coefficient, removing the evaporated moisture more effectively.
Surface area available for evaporation: A larger surface area allows for a higher overall rate of evaporation. Under constant drying conditions (constant air temperature, humidity, and flow rate), the rate of evaporation per unit area of the drying surface remains constant. 
Step 3: Analyze the influence of solid thickness on the drying rate during the constant rate period.
As long as the surface of the solid remains saturated with moisture, the rate of evaporation occurs from this saturated surface layer. The thickness of the solid does not affect the conditions at the drying surface or the rate at which moisture can be evaporated from this surface. The moisture being evaporated is continuously replenished from the interior of the solid by capillary action and diffusion, keeping the surface wet. Therefore, during the constant rate period, the rate of drying is determined by the rate at which moisture can be removed from the saturated surface by the surrounding air, which is independent of the solid's thickness. 
Step 4: Evaluate the given options.
(1) Directly proportional to the solid thickness: This is incorrect. The thickness does not limit the evaporation rate as long as the surface is saturated.
(2) Inversely proportional to the solid thickness: This is also incorrect for the same reason.
(3) Independent of solid thickness: This is correct. The rate of drying is governed by the external conditions and the surface area during the constant rate period.
(4) Directly proportional to the square of solid thickness: This is incorrect and has no physical basis for the constant rate drying. 
Step 5: Conclude the relationship between the drying rate and solid thickness during the constant rate period.
The rate of drying during the constant rate period, when drying occurs from all surfaces, is independent of the solid thickness, as long as the surface remains saturated with moisture.