The air exerts a pressure on the all sides of the bottle.  a) The bottle is heated. What happens to the pressure inside the bottle? Explain your answer

Understanding the Effect of Temperature on Pressure

1. Concept of Pressure in Gases: According to the ideal gas law, pressure (P), volume (V), and temperature (T) of a gas are related by the equation $PV = nRT$, where $n$ is the number of moles of gas, and $R$ is the gas constant. This relationship shows that if the volume is constant (as it is in a sealed bottle), an increase in temperature will result in an increase in pressure.

2. Heating the Bottle: When the bottle is heated, the temperature of the air molecules inside increases. As temperature rises, the kinetic energy of the gas molecules also increases. They move faster and collide with the walls of the bottle more frequently and with greater force.

3. Impact on Pressure: Since the volume of the bottle remains constant and the number of molecules doesn’t change, the increase in temperature leads to a corresponding increase in pressure. Mathematically, if the temperature increases, according to Charles's Law, the pressure will increase.

4. Summary of Findings: Therefore, heating the bottle increases the pressure inside because the gas molecules inside the bottle move more rapidly due to the increase in temperature, thus colliding more often and with greater force against the walls of the bottle.

In conclusion, when the bottle is heated, the pressure inside it increases due to the rise in temperature, leading to increased kinetic energy and more forceful collisions of gas molecules with the walls of the bottle.