Q1: A solid is being dried in the linear drying rate regime from moisture content X_o to X_F. The drying rate is zero at X = 0 and the critical moisture content is the same as the initial moisture X_o. The drying time for M = (L_s/AR_c) is (where, L = total mass of dry solid, A = total surface area for drying R_c = Constant maximum drying rate per unit area X = moisture content (in mass of water/mass of dry solids))

ANS:D - MX_o ln(X_o/X_F)

In the linear drying rate regime, the drying rate is constant, and the rate of moisture removal is directly proportional to the moisture content difference between the initial moisture content (𝑋0X0​) and the final moisture content (𝑋𝐹XF​). The drying time (𝑡t) can be calculated using the equation: 𝑡=𝐿𝑠𝐴⋅𝑅𝑐t=A⋅Rc​Ls​​ Where:

• 𝐿𝑠Ls​ = total mass of dry solid
• 𝐴A = total surface area for drying
• 𝑅𝑐Rc​ = Constant maximum drying rate per unit area

Given that the drying rate is constant in the linear drying rate regime, we can integrate this rate equation to find the time required to dry the solid from an initial moisture content (𝑋0X0​) to a final moisture content (𝑋𝐹XF​): 𝑡=∫𝑋0𝑋𝐹1𝑀 𝑑𝑋t=∫X0​XF​​M1​dX 𝑡=1𝑀∫𝑋0𝑋𝐹 𝑑𝑋t=M1​∫X0​XF​​dX 𝑡=1𝑀(𝑋𝐹−𝑋0)t=M1​(XF​−X0​) 𝑡=𝑀(𝑋0−𝑋𝐹)𝑀t=MM(X0​−XF​)​ 𝑡=𝑋0−𝑋𝐹t=X0​−XF​ Therefore, the drying time for 𝑀=(𝐿𝑠𝐴⋅𝑅𝑐)M=(A⋅Rc​Ls​​) is 𝑀(𝑋0−𝑋𝐹)M(X0​−XF​). So, the correct option is: 𝑀(𝑋0−𝑋𝐹)M(X0​−XF​).