In an adiabatic expansion the product of pressure and volume :

Options

A. decreases
B. increases
C. remains constant
D. first increases then decreases.

Explanation

To solve the question regarding the behavior of the product of pressure and volume during an adiabatic expansion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Adiabatic Process**:
- An adiabatic process is one in which no heat is exchanged with the surroundings. In this case, the internal energy of the gas changes due to work done on or by the gas.

2. **Internal Energy and Temperature**:
- In an adiabatic expansion, the internal energy of the gas decreases. For an ideal gas, the internal energy is directly related to its temperature. Therefore, if the internal energy decreases, the temperature of the gas also decreases.

3. **Ideal Gas Law**:
- The ideal gas law is given by the equation \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the temperature.

4. **Effect of Temperature on PV**:
- Since \( n \) and \( R \) are constants, if the temperature \( T \) decreases during the adiabatic expansion, the product \( PV \) must also decrease. This is because, for a fixed amount of gas, a decrease in temperature leads to a decrease in the product \( PV \).

5. **Conclusion**:
- Therefore, in an adiabatic expansion, the product of pressure and volume decreases.

### Final Answer:
The product of pressure and volume in an adiabatic expansion decreases.

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