How Does a Decrease in Temperature Affect the Pressure of a Contained Gas?

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As opposed to molecules in a liquid or solid, those in a gas can move freely in the space in which you confine them. They fly about, occasionally colliding with one another and with the container walls. The collective pressure they exert on the container walls depends on the amount of energy they have. They derive energy from the heat in their surroundings, so if the temperature goes up, so does the pressure. In fact, the two quantities are related by the ideal gas law.

TL;DR (Too Long; Didn't Read)

In a rigid container, the pressure exerted by a gas varies directly with temperature. If the container isn't rigid, both volume and pressure vary with temperature according to the ideal gas law.

The Ideal Gas Law

Derived over a period of years through the experimental work of a number of individuals, the ideal gas law follows from Boyle's law and the Charles and Gay-Lussac law. The former states that, at a given temperature (T), the pressure (P) of a gas multiplied by the volume (V) it occupies is a constant. The latter tells us that when the mass of the gas (n) is held constant, the volume is directly proportional to the temperature. In its final form, the ideal gas law states:


where R is a constant called the ideal gas constant.

If you keep the mass of the gas and the volume of the container constant, this relationship tells you that pressure varies directly with temperature. If you were to graph various values of temperature and pressure, the graph would be a straight line with a positive slope.

What if a Gas Isn't Ideal

An ideal gas is one in which the particles are assumed to be perfectly elastic and do not attract or repel one another. Moreover, the gas particles themselves are assumed to have no volume. While no real gas fulfills these conditions, many come close enough to make it possible to apply this relationship. However, you must consider real-world factors when the pressure or mass of the gas becomes very high, or the volume and temperature become very low. For most applications at room temperature, the ideal gas law provides a good enough approximation of the behavior of most gases.

How Pressure Varies With Temperature 

As long as the volume and mass of the gas are constant, the relationship between pressure and temperature becomes:


where K is a constant derived from the volume, number of moles of gas and the ideal gas constant. If you put a gas that fulfills ideal gas conditions into a container with rigid walls so the volume can't change, seal the container and measure the pressure on the container walls, you will see it decrease as you lower the temperature. Since this relationship is linear, you just need two readings of temperature and pressure to draw a line from which you can extrapolate the pressure of the gas at any given temperature.

This linear relationship breaks down at very low temperatures when the imperfect elasticity of the gas molecules becomes important enough to affect results, but the pressure will still decrease as you lower the temperature. The relationship will also be nonlinear if the gas molecules are large enough to preclude classifying the gas as ideal.

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