Ideal Gas Law - Volume & Temperature Relationship

Hot air balloon pilots use Charles's law to control their altitude
Hot air balloon pilots use Charles's law to control their altitude | Source

Charles's Law

Boyle's Law told us that the volume and pressure of an ideal gas had an inversely proportionate relationship. As one goes up, the other goes down. As it turns out, Charles's law tells us that volume tends to sleep around, since it is also having a directly proportionate relationship with temperature. That dog.

Fortunately for us, Charles's law is a bit more simple. In a situation where the pressure of an ideal gas remains constant, if the volume or temperature goes up, they both go up. Of course this means if one goes down, they both go......ahem....well, you get the idea.

Equation for Charles's Law

The formula for Charles's law is as simple as the definition, but a lot more fun to look at:

There are however, a few other ways to write it. They are less fun:

In each of these equations, V=Volume and T=Temperature. Also, for those of you who aren't sure why somebody started drawing the infinity symbol () then just stopped, that is the symbol for "directly proportionate."

Converting Celsius to Kelvins

  1. Add 273.15 to C, and you now have a measurement in kelvin.

Converting Fahrenheit to Kelvin

  1. Subtract 32 from F
  2. Divide by 9
  3. Multiply by 5
  4. You now have your temperature in Celsius
  5. Follow steps to convert C to kelvin

Formulas for Conversion

Celsius:
273.15+C=k

Fahrenheit:
5/9(F-32)+273.15=k



The Kelvin Scale

Whenever you are dealing with Charles's law, Boyle's Law, or anything else to do with the ideal gas law, it is important to know that you should be using the Kelvin scale for your temperatures. Since the Centigrade and Fahrenheit scales are both just modified measurements meant for ease of every day use, they don't work out well when doing calculations.

To explain further, you must first understand that the Kelvin scale is what we call an absolute thermodynamic scale. In other words, when you get to zero, you have reached absolute-zero: the coldest possible temperature in our universe, the point at which all thermal motions will cease. There is no upper limit to the Kelvin scale. If you ever find yourself in need of a conversion of Centigrade or Fahrenheit to kelvins, the processes are fairly simple.

*Science is not hard at work trying to figure out how to prove the existence of matter that has -13 molecules.

Why Use Kelvins?

As mentioned before, the Kelvin scale will take us from absolute-zero, to infinity. It is a scientific method of measuring heat energy. Centigrade is a system of measurement proportionate to the different stages of water. Zero degrees Celsius is the freezing point of water, where 100 degrees Celsius is the boiling point. Go above or below those two numbers, and water becomes either a solid or a gas.

Fahrenheit has a much more complicated history. It is also far more useless than either of the other two.

The problem with both of these systems? Negative temperatures. You can certainly try to use them, but what happens when your temperature goes below zero? Suddenly you may have a calculation that gives you an impossible negative volume. No worries though, science is hard at work trying to figure out how to prove the existence of matter that has -13 molecules.*

Gas Volume at Absolute-Zero

Now that we're all experts on the relationship between volume and temperature, you may be wondering what happens at absolute-zero. The Kelvin scale may not have negative numbers, but it certainly has a zero. Even with the most basic knowledge of algebra, one can assume that V1T2 = V2T1 where either T1 or T2 is zero, then your formula will be an odd one:

0=0

Yes, zero is definitely equal to zero. Trust me, I Googled it before writing this. If this is true, then the volume of the gas is zero. A volume of zero means we have zero molecules. This just makes zero sense!

There are a few answers to this problem.

  1. The ideal gas law breaks down at the lowest temperatures, making it null and void at absolute zero
  2. Since ideal gasses themselves are only theoretical, then we can say that an ideal gas at any pressure has a volume of zero when the temperature is absolute-zero on the Kelvin scale.
  3. Since zero is nothing, then it still works. A gas with zero volume will obviously have no temperature, and vice versa. The formula tells us simply that the gas we are measuring just...isn't there.

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Comments 1 comment

LisaKoski profile image

LisaKoski 4 years ago from WA

Another great and informative hub. I especially liked the part where you explain why they use Kelvins because I've always kind of wondered about that.

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