The gas law (PV/T) = constant is true for

Options

A. isothermal changes only
B. adiabatic change
C. both isothermal and adiabatic
D. neither isothermal nor adiabatic

Answer

To solve the question regarding the gas law \( \frac{PV}{T} = \text{constant} \), we need to analyze the ideal gas law and its implications for different thermodynamic processes.

### Step-by-Step Solution:

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

2. **Rearranging the Ideal Gas Law**:
From the ideal gas law, we can rearrange the equation to express \( \frac{PV}{T} \):
\[ \frac{PV}{T} = \frac{nR}{T} \]
Since \( n \) (number of moles) and \( R \) (universal gas constant) are constants for a given amount of gas, we can conclude that:
\[ \frac{PV}{T} = \text{constant} \]

3. **Identifying the Types of Processes**:
- **Isothermal Process**: This is a process that occurs at a constant temperature (T is constant). Hence, \( PV \) will vary such that \( \frac{PV}{T} \) remains constant.
- **Adiabatic Process**: In this process, there is no heat exchange with the surroundings. While temperature may change, the relationship \( PV = nRT \) still holds, and thus \( \frac{PV}{T} \) remains constant as long as the number of moles and the gas constant are unchanged.

4. **Conclusion**:
Since the relationship \( \frac{PV}{T} = \text{constant} \) holds true for both isothermal and adiabatic processes, the correct answer to the question is:
- **Option C: Both isothermal and adiabatic processes**.