A gas expands in such a manner that its pressure and volume comply with the condition `"PV"^2` = constant. Will the gas cool or get heated on expansion?

Explanation

To determine whether the gas will cool or heat up during expansion under the condition \( PV^2 = \text{constant} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Condition**:
We start with the condition \( PV^2 = \text{constant} \). This implies that as the gas expands (increasing volume \( V \)), the product of pressure \( P \) and the square of volume \( V^2 \) remains constant.

2. **Use the Ideal Gas Law**:
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