At constant volume, if pressure is increased, what happens to the temperature of the gas?

When the pressure of a gas is increased at constant volume, the temperature of the gas must increase as well. This relationship is explained by Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature when the volume is kept constant.

In mathematical terms, this relationship can be expressed as ( P \propto T ) or ( \frac{P}{T} = k ), where ( P ) is the pressure, ( T ) is the absolute temperature (measured in Kelvin), and ( k ) is a constant. When the pressure increases, it necessitates a corresponding increase in temperature to maintain this proportionality.

To visualize this, think of a confined gas (like one in a sealed container) that is not allowed to expand. As you increase the pressure (for instance, by compressing the gas), you are essentially forcing the gas molecules into a smaller space, which means they collide more frequently and with greater energy. This increase in molecular activity translates to a higher temperature.

Therefore, when pressure rises at constant volume, the temperature also rises, confirming that the correct choice is indeed the increase in temperature.