200 kg of solids (on dry basis) is subjected to a drying process for a period of 5000 seconds. The drying occurs in the constant rate period with the drying rate as, N_c = 0.5 × 10^-3 kg/m².s. The initial moisture content of the solid is 0.2 kg moisture/kg dry solid. The interfacial area available for drying is 4 m²/1000 kg of dry solid. The moisture content at the end of the drying period is (in kg moisture/kg dry solid)

We are given:

Dry solid mass,
𝑊
=
200
 
kg
W=200kg

Drying time,
𝑡
=
5000
 
s
t=5000s

Drying rate during constant rate period,
𝑁
𝑐
=
0.5
×
10
−
3
 
kg/m
2
⋅
s
N
c
​
=0.5×10
−3
kg/m
2
⋅s

Initial moisture content,
𝑋
𝑖
=
0.2
 
kg moisture/kg dry solid
X
i
​
=0.2kg moisture/kg dry solid

Interfacial area per 1000 kg dry solid = 4 m²
So for 200 kg dry solid:

𝐴
=
4
1000
×
200
=
0.8
 
m
2
A=
1000
4
​
×200=0.8m
2

Step 1: Calculate total moisture removed
Moisture removed
=
𝑁
𝑐
×
𝐴
×
𝑡
=
0.5
×
10
−
3
×
0.8
×
5000
=
2
 
kg moisture
Moisture removed=N
c
​
×A×t=0.5×10
−3
×0.8×5000=2kg moisture
Step 2: Convert moisture removed to per kg dry solid basis
Moisture removed per kg dry solid
=
2
200
=
0.01
 
kg moisture/kg dry solid
Moisture removed per kg dry solid=
200
2
​
=0.01kg moisture/kg dry solid
Step 3: Find final moisture content
𝑋
𝑓
=
𝑋
𝑖
−
Moisture removed per kg dry solid
=
0.2
−
0.01
=
0.19
 
kg moisture/kg dry solid
X
f
​
=X
i
​
−Moisture removed per kg dry solid=0.2−0.01=0.19kg moisture/kg dry solid
But this contradicts the given options — none match 0.19. So let's recheck the calculation:

Correct Approach:
Moisture removed
=
𝑁
𝑐
⋅
𝐴
⋅
𝑡
=
0.5
×
10
−
3
×
0.8
×
5000
=
2
 
kg
Moisture removed=N
c
​
⋅A⋅t=0.5×10
−3
×0.8×5000=2kg
So the total moisture removed is 2 kg.

Initial moisture in the solid:

Initial moisture
=
𝑋
𝑖
×
𝑊
=
0.2
×
200
=
40
 
kg
Initial moisture=X
i
​
×W=0.2×200=40kg
Final moisture:

40
−
2
=
38
 
kg
40−2=38kg
Final moisture content (per kg dry solid):

𝑋
𝑓
=
38
200
=
0.19
 
kg moisture/kg dry solid
X
f
​
=
200
38
​
=0.19kg moisture/kg dry solid
Again, this is 0.19, which is not listed.

Conclusion:
There might be an issue with the drying rate unit or area conversion in the problem. Let's try again by verifying drying area:

Area = 4 m² per 1000 kg dry solid
For 200 kg:

𝐴
=
4
1000
×
200
=
0.8
 
m
2
A=
1000
4
​
×200=0.8m
2

Everything checks out.

So the correct final moisture content is:

0.19
 
kg moisture/kg dry solid
0.19kg moisture/kg dry solid
​

Since this is not among the options, and the closest listed option is 0.15, none of the provided options is correct based on the given data.

👉 Answer: None of the above (Correct value is 0.19 kg moisture/kg dry solid)

Take 4m2/100kg
For 200kg area will be 200kg *(4 m2/100 kg)=8 m2
500=200/(8*0.5*10^-3)(xi-xf) xi=0.2
Xf=0.1

According to the answer data should be 4 m2/100 kg. So do make corrections

If u provide step it would be easy to understand