A process `AtoB` is difficult to occur directly instead it takes place in the three successive steps.
`DeltaS(AtoC)=50e.u.`
`DeltaS(CtoD)=30e.u.`
`DeltaS(BtoD)=20e.u.` where e.u. is entropy unit. Then the entropy change for the process `DeltaS(AtoB)` is:

Options

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

Answer

To find the total entropy change for the process from A to B, we can use the given values of entropy changes for the individual steps. The steps are as follows:

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

2. **Calculate the total entropy change from A to D:**
- The total change in entropy from A to D can be calculated by adding the entropy changes from A to C and C to D:
\[ ΔS(A to D) = ΔS(A to C) + ΔS(C to D) = 50 \, \text{e.u.} + 30 \, \text{e.u.} = 80 \, \text{e.u.} \]

3. **Reverse the process from D to B:**
- Since we need to find the change in entropy from A to B, we need to consider the reverse of the process from B to D. The change in entropy for the reverse process is negative:
\[ ΔS(D to B) = -ΔS(B to D) = -20 \, \text{e.u.} \]

4. **Combine the changes to find ΔS(A to B):**
- Now, we can find the total change in entropy from A to B by combining the changes from A to D and D to B:
\[ ΔS(A to B) = ΔS(A to D) + ΔS(D to B) = 80 \, \text{e.u.} - 20 \, \text{e.u.} = 60 \, \text{e.u.} \]

Thus, the total entropy change for the process from A to B is:
\[ \Delta S(A to B) = 60 \, \text{e.u.} \]