### Physics: The Ideal Gas law

Imagine for a moment that we recently came into possession of an inflated balloon. Inside of this balloon, there are trillions of individual gas particles flowing freely in all directions. We like this balloon and we are worried about it popping, and so we decide to calculate the force that all those gas particles are exerting on the surface of the balloon. We call this force pressure.

Pressure can be defined as force divided by area. For anyone wishing to brush up on forces, they can look back at the post on Newton’s Laws. In the context of our balloon, at any given moment, some gas particles are bouncing off the interior surface of the balloon. each bounce applies a force to the balloon that can be measured. But how?

### Gay-Lussac’s Law

Conceptually, what variables would we guess have an impact on pressure? Well, we know that if the gas particles are moving fast they will bounce into the balloon with increased force. This is just F = MA. So faster particles equal more pressure. However, there is no easy way to calculate the individual movements of trillions upon trillions of gas particles. Instead, we take the average of all those movements. Lucky for us we already have a measure of the average energy in a system: temperature. Temperature can be thought of as the total energy divided by the number of particles in a system. We now have a good idea that pressure and temperature are related.

Gay-Lussac’s law: The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas’s absolute temperature.

P/T = k

P is the pressure of the gas

T is the temperature of the gas

k is a constant

To get from average energy per particle (temperature), to total energy in the system (pressure), we simply need to multiply temperature by the number of gas particles in the system, which is measured in moles.

Combining these ideas, we work out that pressure is proportional to temperature multiplied by moles. The more particles we have, and the faster those individual particles are moving, the more pressure we will have.

### Boyle’s law

Can we think of any other variables that would have an effect on pressure? How about the size of the container, or in this case the size of the balloon? If we hold the temperature and the amount of particles constant, but reduce the volume of the balloon, what will happen? Well, all of those particles will bump into the surface at an increased rate. There will be more force being applied to less area. We know that if we have more force and less area, the pressure will increase so we can now say that pressure is inversely related to volume.

Boyle’s law: The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if temperature and amount of gas remain constant.

PV = k

P is the pressure of gas

V is the volume of gask is a constant

### Ideal gas law

When we combine these ideas together, we derive the idea gas law. Pressure is directly proportional to the temperature of a system, the amount of substance in the system, and the volume of the system. A constant needs to be added to the formula to make sure all the units work out. Pressure is measured in newtons per squared meter.

Ideal gas law: The state of an amount of gas is determined by its pressure, volume, and absolute temperature.

PV = nRT

P is the pressure

V is the volume

n is the moles

R is the gas constant

T is the temperature

### What is an ideal gas?

An ideal gas assumes that all of the gas particles in a container have inconsequential volumes and that they don’t attract or repeal each other. These assumptions tend to hold up when temperatures are high and pressure is low. At lower temperatures, inter-molecular attractions become more powerful. At higher pressures, the average distance between molecules decreases and their volume have more of an impact.

The ideal gas assumption turns out to be a good approximation of many gases under many conditions.

### Applications of the ideal gas law

When we push down on a car’s accelerator, drops of gasoline and air are sprayed into the engine. This mixture goes into the cylinder where a spark ignites it. The heat from this explosion increases the volume of the gas, which forces the piston down into the cylinder. This opens an outlet valve, causing gas to be released and the piston to rise, which in turn opens an inlet valve that repeats the process. The reactions of the gasoline and air to changes in pressure, temperature, and volume are what move the piston, which turns a crankshaft that causes the wheels to rotate.

When breath in, the diaphragm expands, causing the volume of the thoracic cavity to increase, which in turn decreases the pressure in the lungs, creating a vacuum. This reduction in pressure pulls air into the lungs. When we exhale, the volume contracts and the pressure forces air out of the lungs. It’s the inverse relationship of pressure and volume that allows us to continue breathing.

### Conclusion

The ideal gas law is an equation of state. In physics, an equation of state is an equation describing the state of matter under a given set of physical conditions. From these equations, we are able to describe the properties of fluids, solids, and even the make up of stars.

These equation’s weren’t always known. They were derived, over the years, through a process of observation and experimentation. Physics, more than anything else, teaches us the problem solving skills required to form these understandings. As was the case with the ideal gas law, all problems in life require us to identify the variables and relationships involved within them. We start small, solving everyday problems, and piece by piece we build up an understanding of the universe.

References:

https://www.khanacademy.org/science/chemistry/gases-and-kinetic-molecular-theory/ideal-gas-laws/v/ideal-gas-equation-pv-nrt

https://en.wikipedia.org/wiki/Ideal_gas_law