To determine which of the given statements about thermodynamic processes are correct, let's analyze each statement step by step:
### Step 1: Analyze Statement 1
**Statement 1:** "Reversible adiabatic process is isoentropic."
- An adiabatic process is one in which no heat is exchanged with the surroundings (Q = 0).
- A reversible adiabatic process is indeed isoentropic, meaning the entropy of the system remains constant throughout the process.
- Therefore, **Statement 1 is correct.**
### Step 2: Analyze Statement 2
**Statement 2:** "ΔS system for irreversible adiabatic compression is greater than 0."
- For an irreversible adiabatic process, while the heat exchange (Q) is still 0, the change in entropy (ΔS) can be calculated using the relationship ΔS = Q/T.
- However, since the process is irreversible, the entropy of the system will increase due to the irreversibility, even though Q = 0.
- Hence, ΔS system for irreversible adiabatic compression is indeed greater than 0.
- Therefore, **Statement 2 is correct.**
### Step 3: Analyze Statement 3
**Statement 3:** "ΔS system for free expansion is 0."
- In a free expansion, a gas expands into a vacuum without doing work and without heat exchange (Q = 0).
- However, the entropy of the system does increase because the gas occupies a larger volume and has more microstates available.
- Thus, ΔS system for free expansion is not 0; it is greater than 0.
- Therefore, **Statement 3 is incorrect.**
### Step 4: Analyze Statement 4
**Statement 4:** "ΔS system for irreversible isothermal compression is greater than 0."
- In an isothermal process, the temperature remains constant, and for an irreversible process, the system does not reach equilibrium.
- Even though the system is compressing and work is being done, heat is still exchanged with the surroundings.
- The change in entropy for an irreversible isothermal process is greater than 0 because the system is not in equilibrium and the process is irreversible.
- Therefore, **Statement 4 is correct.**
### Conclusion
After analyzing all statements, we find that:
- **Correct Statements:** 1, 2, and 4
- **Incorrect Statement:** 3
### Final Answer
The correct options are 1, 2, and 4.
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