The direct conversion of A to B is difficult. Hence it is carried out by the following shown path:
`DeltaS(ArarrC)=50e.u.,DeltaS(CrarrD)=30e.u,`
`DeltaS(BrarrD)=20e.u` where e.u is entropy unit.
Then `DeltaS(ArarrB)`,

Options

A. `+100e.u`
B. `+60e.u`
C. `-100e.u`
D. `-60e.u`

Explanation

To find the change in entropy (ΔS) for the direct conversion of A to B, we can break down the process into the steps provided in the question. We will use the given entropy changes for each step in the process.

### Step-by-Step Solution:

1. **Identify the given values:**
- ΔS(A → C) = 50 e.u.
- ΔS(C → D) = 30 e.u.
- ΔS(B → D) = 20 e.u.

2. **Determine the reverse process for B to D:**
- Since we need to find ΔS(A → B), we will consider the path A → C → D → B.
- The change in entropy for the reverse process (D → B) will be negative:
- ΔS(D → B) = -ΔS(B → D) = -20 e.u.

3. **Combine the entropy changes:**
- Now we can add the entropy changes for the entire path A → C → D → B:
\[ ΔS(A → B) = ΔS(A → C) + ΔS(C → D) + ΔS(D → B) \]
- Substitute the values:
\[ ΔS(A → B) = 50 \text{ e.u.} + 30 \text{ e.u.} - 20 \text{ e.u.} \]

4. **Calculate the total change in entropy:**
\[ ΔS(A → B) = 50 + 30 - 20 = 60 \text{ e.u.} \]

### Final Answer:
The change in entropy for the conversion from A to B is:
\[ ΔS(A → B) = 60 \text{ e.u.} \]

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