What happens to the pressure of a gas when the volume is decreased and the temperature is increased?

Updated December 05, 2020

By Chris Deziel

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.

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.

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:

PV=nRT

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.

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.

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

P=KT

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.

How cool is it to change your state? Freeze me; I am ice. Heat me; I am water. Boil me; I am steam. I have different forms and states: I am Matter!

The Different States of Matter (Photo Credit : VectorMine/Shutterstock)

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The versatility of ‘Matter’

Simply put, the definition of matter is something that carries mass and occupies space. There are four fundamental states of matter: Solid, Liquid, Gas, and Plasma.

Arrangement of molecules in different states of matter (Photo Credit : udaix/Shutterstock)

Liquids:

These are fluidic, have a definite volume, no definite shape (takes the shape of the container), and are incompressible. Moderate intermolecular forces hold the molecules together with weak intermolecular spaces. The molecules in liquid move with moderate kinetic energy. Liquids possess properties of capillary action, viscosity, and surface tension.

Gases:

Inter- molecular spaces in gases (Photo Credit : Arisa_J/Shutterstock)

Plasma:

The most abundant state of matter in the universe is plasma or superheated matter. 99% of the matter in the Universe is in the plasma state. When energy is passed through neutral gas, the electrons are removed to form both positively and negatively charged ions. It has neither shape nor volume. Plasma makes up the sun and stars.

(Photo Credit : Quardia/Shutterstock)

What determines the state of Matter?

Matter has a specific state at a given temperature and pressure. The two factors that regulate its state are:

1. Temperature (explained by Charles’ Law)
2. Pressure (explained by Boyles’ Law)

Understanding the effect of temperature on the States of Matter

At atmospheric pressure, water exists as a liquid at temperatures between 0ᵒC to 100ᵒC, as water vapor (gas) beyond 100ᵒC, and as ice (solid) at 0ᵒC and below. The temperature ranges in which substances exist in a particular state vary for each substance. We know that water has three states, but what about other elements and compounds? Do iron, oxygen, and calcium chloride exist in three states? The emphatic answer is: “All matter exists in different states, depending on the temperature and pressure”. From the above, oxygen is a gas at > -182ᵒC, while iron is a gas at 2860ᵒC. All matter can exist in the three states, but the temperatures at which they attain each state vary broadly.

Charles’s Law governs the States of Matter

Charles’s Law states that the volume of a fixed amount of gas is directly proportional to its absolute temperature if the pressure remains constant.

Charles’s Law postulating the relationship between Temperature and Volume (Photo Credit : udaix/Shutterstock)

Understanding the effect of pressure on the States of Matter

As mentioned earlier, pressure is another critical factor that determines the state of matter. This principle is used in the manufacture of liquid N2 and dry ice (solid carbon dioxide). Gaseous Nitrogen will become a liquid when pressure is increased on the gas. On the other hand, you can make water boil at room temperature by decreasing the pressure enough. So, pressure and temperature are in an inverse relationship. Liquid N2 and dry ice are manufactured by applying pressure on the gases N2 and CO2 to change their state from gas to liquid and gas to solid, respectively.

Liquid N2 (Photo Credit : Suslov Denis/Shutterstock)

Dry Ice (Photo Credit : Kollawat Somsri/Shutterstock)

Boyle’s Law governs the States of Matter

As mentioned earlier, there is an inverse relationship between pressure and temperature, which is governed by Boyle’s law. According to the law, the volume of a gas increases as the pressure decreases, at a constant temperature.

Boyle’s Law postulating the relationship between Pressure and Volume (Photo Credit : udaix/Shutterstock)

How is dry ice formed?

In dry ice manufacturing, the pressure on CO2 gas is reduced from 1 atmospheric (1 atm) to 5.11. At this pressure, and at a constant -56ᵒC, gaseous CO2 becomes solid CO2 with a very transient liquid state. The specific temperature and pressure at which three states of any matter are in equilibrium is called its triple point.

Triple point: The temperature and pressure at which the solid, liquid, and vapor phases of a pure substance can coexist in equilibrium (Photo Credit : magnetix/Shutterstock)

Conclusions

The states of matter are continuously recycled, and temperature and pressure control the phase transitions. The temperature and pressure at which all the states coexist is called the triple point. A finely orchestrated process between temperature, volume, and pressure determines the state of any matter.

Suggested Reading

References

1. Scientific American (Link 1)
2. Scientific American (Link 2)

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