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)

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

A. M (Xo - XF)

B. M (Xo/XF)

C. M ln(Xo/XF)

D. MXo ln(Xo/XF)

Given:
**Drying occurs in the linear drying rate regime.

Drying rate is constant until moisture reaches critical level.

Critical moisture content = Initial moisture content
X
o
X
o
​

→ So the falling rate period is absent.

Drying rate is constant = R_c

Final moisture content =
X
F
X
F
​


Formula for drying time in the constant rate period:
t
=
L
s
A
R
c
(
X
o
−
X
F
)
t=
AR
c
​

L
s
​

​
(X
o
​
−X
F
​
)
Let:

M
=
L
s
A
R
c
M=
AR
c
​

L
s
​

​

Then:

t
=
M
(
X
o
−
X
F
)
t=M(X
o
​
−X
F
​
)
✅ Correct Answer:
A. M (Xₒ - X𝐹)

Why others are wrong:
B. M (Xo/XF) → This form arises in log-based decay or proportional rate cases, not constant rate.

C. M ln(Xo/XF) → Logarithmic forms arise in falling rate period, not constant rate.

D. MXo ln(Xo/XF) → Also from falling rate period assumptions.

How does the Xnod factor is additional in D option?