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 determine for which condition the gas law \( PV = \text{constant} \) holds true, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**: The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the universal gas constant, and \( T \) is the absolute temperature in Kelvin.

2. **Identify the Condition for \( PV \) to be Constant**: For the equation \( PV = \text{constant} \) to hold, the right-hand side of the ideal gas law, \( nRT \), must also be constant. This implies that both \( n \) (the number of moles) and \( T \) (the temperature) must remain constant.

3. **Consider the Isothermal Process**: In thermodynamics, an isothermal process is defined as one that occurs at a constant temperature. Since \( T \) is constant in this process, and assuming the number of moles \( n \) is also constant (as we are considering a closed system), we can conclude that:
\[ nRT = \text{constant} \]
Therefore, under these conditions, we can say that:
\[ PV = \text{constant} \]

4. **Conclusion**: The gas law \( PV = \text{constant} \) is true specifically for an isothermal process, where the temperature remains constant.

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