Temperature plays a big role in how gas particles move around. This idea comes from something called the kinetic theory of gases. According to this theory, gas is made up of tiny particles that are always moving. Here's how temperature affects these particles:

1. Kinetic Energy: The average energy of gas particles, known as kinetic energy, goes up when the temperature goes up. This is shown in a simple formula:

   $\text{KE}_{\text{avg}} = \frac{3}{2} k T$

   In this formula, $k$ is a special number called the Boltzmann constant, and $T$ is the temperature measured in Kelvin. When the temperature increases, the average energy of the gas particles increases too. This means they move faster.

2. Speed of Particles: We can also measure how fast gas particles move using something called the root-mean-square speed ($v_{\text{rms}}$). The formula for this is:

   $v_{\text{rms}} = \sqrt{\frac{3kT}{m}}$

   Here, $m$ is the mass of a single particle. For example, at room temperature (about 293 K), air molecules move at a speed of about 500 meters per second. That's really fast!

3. Pressure and Temperature Relationship: There's a rule called Gay-Lussac's Law that explains how pressure and temperature are connected. It says that when the volume stays the same, the pressure of a gas goes up when the temperature goes up:

   $P \propto T$

   This means that as temperature increases, the particles bump into the walls of their container more often and more forcefully, which raises the pressure.

To sum it all up, when the temperature goes up:

• Gas particles have more energy.
• They move faster.
• They create more pressure.

Understanding how temperature affects gas helps us with many things, from basic activities like breathing to important industries like engines and refrigerators.