The gas law PV=constant is true for

Options

A. Isothermal changes only
B. Adiabatic change only
C. Both isothermal and adiabatic changes
D. Neither isothermal nor adiabatic changes.

Answer

To solve the question regarding the gas law \( PV = \text{constant} \), we will analyze the conditions under which this law holds true.

### Step-by-Step Solution:

1. **Understanding the Gas Law**: The equation \( PV = \text{constant} \) indicates a relationship between pressure (P) and volume (V) of a gas. This relationship suggests that if one variable changes, the other must change in such a way that their product remains constant.

2. **Identifying Types of Processes**:
- **Isothermal Process**: This is a process that occurs at a constant temperature. In an isothermal process, the internal energy of the gas remains constant, and any heat added to the system is used to do work.
- **Adiabatic Process**: This is a process where no heat is exchanged with the surroundings. In this case, the temperature of the gas can change as work is done on or by the gas.

3. **Analyzing the Isothermal Process**:
- In an isothermal process, since the temperature remains constant, the relationship \( PV = nRT \) implies that if the temperature (T) is constant, then \( PV \) must also remain constant. Thus, for an isothermal process, \( PV = \text{constant} \) holds true.

4. **Analyzing the Adiabatic Process**:
- In an adiabatic process, the temperature changes as work is done on or by the gas. Therefore, the relationship \( PV \) does not remain constant because the internal energy changes, leading to a change in temperature. Thus, \( PV = \text{constant} \) does not hold true for adiabatic processes.

5. **Conclusion**: Based on the analysis, the gas law \( PV = \text{constant} \) is true only for isothermal processes, where the temperature remains constant.

### Final Answer:
The gas law \( PV = \text{constant} \) is true for **isothermal changes only**.

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