Which of the following regarding the said processes is (are) correct?

Options

A. Expansion of an ideal gas against vaccum is always reversible
B. A spontaneous proces is always irreversible
C. In a reversible thermodynamic process, system always remains in equilibrium with surroundings
D. If a system containing ideal gas in a piston udergoes expansion from a given initial state to the same final volume,the surroundings loses more heat if expansion is carried out irreversibly rather reversibly

Explanation

To solve the question regarding which statements about the processes are correct, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement 1: Expansion of an ideal gas against vacuum is always reversible.**
- **Analysis:** When an ideal gas expands against a vacuum, there is no opposing pressure. This means that the gas can expand freely without doing any work against an external pressure. Such a process is spontaneous and occurs without any resistance, making it irreversible.
- **Conclusion:** This statement is **incorrect**.

2. **Statement 2: A spontaneous process is always irreversible.**
- **Analysis:** A spontaneous process is one that occurs naturally without needing to be driven by an external force. While many spontaneous processes are indeed irreversible (like the mixing of sugar in water), there are also spontaneous processes that can be reversible under certain conditions. For example, the melting of ice at 0°C can be reversible if the conditions allow for the ice to refreeze.
- **Conclusion:** This statement is **incorrect**.

3. **Statement 3: In a reversible thermodynamic process, the system always remains in equilibrium with its surroundings.**
- **Analysis:** A reversible process is defined as one that can be reversed by an infinitesimal change in a variable, and during such a process, the system is in equilibrium with its surroundings at all times. This means that the system can be returned to its original state without any net change in the universe.
- **Conclusion:** This statement is **correct**.

4. **Statement 4: If a system containing an ideal gas in a piston undergoes expansion from a given initial state to a final volume, the surroundings lose more heat if the expansion is carried out irreversibly rather than reversibly.**
- **Analysis:** In a reversible expansion, the system does work on the surroundings and absorbs heat from them. In an irreversible expansion, the system does less work and typically loses less heat to the surroundings. Therefore, the surroundings do not lose more heat in the case of irreversible expansion; they lose less heat compared to a reversible process.
- **Conclusion:** This statement is **incorrect**.

### Final Summary of Correct Statements:
- The only correct statement is **Statement 3**.