Which of the following represents the Boyle's Law?

$V ∝ \frac{1}{P}$ (at constant $T$)

The correct answer is option 2. $V ∝ \frac{1}{P}$ (at constant $T$).

Boyle's Law describes the relationship between the volume (V) and pressure (P) of a given amount of gas at constant temperature (T). It states that when the temperature of a gas remains constant, the volume of the gas is inversely proportional to its pressure. In other words, as the pressure exerted on a gas increases, its volume decreases, and vice versa, as long as the temperature remains constant.

Mathematically, Boyle's Law can be expressed as:

\[ V \propto \frac{1}{P} \]

where:

\( V \) represents the volume of the gas,

\( P \) represents the pressure of the gas,

The symbol \( \propto \) denotes proportionality.

This equation indicates that as pressure (P) increases, volume (V) decreases, and as pressure decreases, volume increases, while keeping the temperature constant.

This law is commonly observed in everyday situations, such as inflating a balloon. When you blow air into a balloon, you increase the pressure inside the balloon, causing its volume to expand. Conversely, when you release air from the balloon, the pressure inside decreases, causing the balloon to deflate.

Understanding Boyle's Law is essential in various fields, including chemistry, physics, and engineering, as it helps explain the behavior of gases under different pressure and volume conditions.