If a balloon is heated while the pressure remains constant, the volume of air inside the balloon will increase. This is because as the temperature of the air increases, the average kinetic energy of the air molecules also increases. This means that the air molecules move faster and collide with the walls of the balloon more frequently and with greater force, causing the balloon to expand.

Mathematically, this relationship between temperature and volume at constant pressure is described by Charles's law, which states that the volume of a gas is directly proportional to its temperature. In equation form, this can be expressed as:

```

V ∝ T

```

or

```

V = kT

```

where:

* V is the volume of the gas

* T is the temperature of the gas

* k is a constant

According to Charles's law, if the pressure remains constant, the volume of the gas will increase in direct proportion to the increase in temperature. Conversely, if the temperature decreases, the volume of the gas will decrease.