Gaseous system is placed with pressure `P_(1)`, volume `V_(1)` and temperature `T_(1)`, it has undergone thermodynamic changes where temperature is remaining constant, it is

Options

A. Adiabatic process
B. Isothermal process
C. Isobaric process
D. Isochoric process

Answer

To solve the problem regarding the gaseous system that undergoes thermodynamic changes while maintaining a constant temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Conditions**: The problem states that the gaseous system has initial conditions defined by pressure \( P_1 \), volume \( V_1 \), and temperature \( T_1 \). The key point here is that the temperature remains constant during the process.

2. **Understand the Types of Thermodynamic Processes**:
- **Isothermal Process**: This is a process in which the temperature remains constant. For an ideal gas undergoing an isothermal process, the relationship between pressure and volume is given by Boyle's Law:
\[ P_1 V_1 = P_2 V_2 \]
- **Adiabatic Process**: This process occurs without heat transfer, and the temperature changes during this process.
- **Isobaric Process**: This process occurs at constant pressure, meaning the pressure does not change.
- **Isochoric Process**: This process occurs at constant volume, meaning the volume does not change.

3. **Determine the Relevant Process**: Since the temperature is constant in this scenario, we can conclude that the process is an **isothermal process**.

4. **Apply the Ideal Gas Law**: In an isothermal process for an ideal gas, the pressure and volume are inversely related. If the volume changes, the pressure will adjust accordingly to maintain the relationship defined by Boyle's Law.

5. **Conclusion**: Since the temperature remains constant, the correct answer to the question is that the gaseous system undergoes an **isothermal process**.

### Final Answer:
The gaseous system undergoes an **isothermal process**.

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