Which statements are correct for a process involving an ideal gas?

Options

A. `(Delta S)_("Isothermal, sys") = 2.303 nRlog (V_(f))/(V_(i))`
B. `(Delta S)_("adiabatic, rev") = 0`
C. `(Delta S)_("Total, irr") lt 0`
D. `(Delta S)_("Total, adiabatic, rev") = 0`

Answer

To determine which statements are correct for a process involving an ideal gas, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement A: ΔS isothermal**
- For an isothermal process involving an ideal gas, the change in entropy (ΔS) can be calculated using the formula:
\[ ΔS = N C_V \ln\left(\frac{T_2}{T_1}\right) + N R \ln\left(\frac{V_2}{V_1}\right) \]
- Since the process is isothermal, the temperature remains constant (T1 = T2), which means:
\[ \ln\left(\frac{T_2}{T_1}\right) = 0 \]
- Therefore, the equation simplifies to:
\[ ΔS = N R \ln\left(\frac{V_2}{V_1}\right) \]
- This indicates that the change in entropy during an isothermal process is dependent on the volume change. Thus, **Statement A is correct**.

2. **Statement B: ΔS adiabatic**
- In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). The change in entropy (ΔS) can be expressed as:
\[ ΔS = \frac{Q}{T} \]
- Since Q = 0, it follows that:
\[ ΔS = 0 \]
- Therefore, **Statement B is correct**.

3. **Statement C: ΔS total in irreversible is always greater than 0**
- The total change in entropy (ΔS_total) for a process is given by:
\[ ΔS_{total} = ΔS_{system} + ΔS_{surroundings} \]
- For irreversible processes, the total change in entropy is always greater than 0, not less than 0. Therefore, **Statement C is incorrect**.

4. **Statement D: ΔS total in adiabatic will be equal to 0**
- In an adiabatic process, while Q = 0, it does not imply that the total change in entropy is 0. The entropy can still increase due to irreversible processes. Thus, **Statement D is incorrect**.

### Summary of Correct Statements:
- **Correct Statements**: A and B
- **Incorrect Statements**: C and D

### Final Answer:
The correct statements for a process involving an ideal gas are **A and B**.