Sample of gases are taken through isothermal and adiabatic process. Choose which of the following diagram correctly represent isothermal and adiabatic process

Options

A.
B.
C.
D.

Answer

To solve the problem of identifying the correct diagrams representing isothermal and adiabatic processes, we need to understand the characteristics of these two thermodynamic processes.

### Step-by-Step Solution:

1. **Understand Isothermal Process**:
- In an isothermal process, the temperature (T) remains constant. This means that any heat added to the system is used to do work, and the internal energy of the system does not change.
- The relationship between pressure (P) and volume (V) for an ideal gas during an isothermal process is given by Boyle's Law: \( PV = \text{constant} \).

2. **Understand Adiabatic Process**:
- In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). The temperature of the gas changes as it expands or compresses.
- The relationship for an ideal gas during an adiabatic process is given by \( PV^\gamma = \text{constant} \), where \( \gamma \) (gamma) is the heat capacity ratio (C_p/C_v).

3. **Analyzing the Graphs**:
- **Graph 1**: Check if it represents an isothermal or adiabatic process. Since it shows constant pressure, it cannot represent an isothermal process (which should show a hyperbolic curve). Thus, this graph is incorrect.
- **Graph 2**: Analyze the temperature lines. If it shows a constant temperature line, it may represent an isothermal process. However, if it shows a constant pressure line, it is incorrect.
- **Graph 3**: Look for a hyperbolic curve indicating an isothermal process (constant temperature). If it shows a curve that decreases in pressure as volume increases, this could be correct.
- **Graph 4**: Similar to Graph 3, check if it shows a hyperbolic curve for isothermal and a steep curve for adiabatic. If it shows a straight line, it is incorrect.

4. **Conclusion**:
- After analyzing all graphs, identify which graph correctly represents the isothermal process (constant temperature) and which one represents the adiabatic process (no heat exchange).
- The correct answer will be the graph that shows the isothermal process as a hyperbolic curve and the adiabatic process as a steeper curve.

### Final Answer:
- The correct representation for the isothermal and adiabatic processes is found in **Option 4**.