Feb 2017

Kinetic Energy of a Molecule

February 23, 2017

If you are brushing up for your exams, you will need to pay attention to the kinetic energy of a molecule and how it interacts with molecular theories of gas. Remember that this will also involve you being familiar with both Boyle’s and Charles’ law, and need you to pay careful attention to how pressure, energy, and temperature work together with the gas model to create these effects. All these will be covered in our JC physics tuition class, so let’s first recap the kinetic molecular theory.

Recapping the Kinetic Molecular Theory

There are a few basics at the heart of Kinetic Molecular theory. These are:

  • Gas molecules are present in large numbers of continuously moving, randomly moving
  • The volume of these molecules is negligible in comparison to the volume the gas occupies
  • While temperature is constant, the kinetic energy of these molecules does not alter. It can be transferred during collisions [which are deemed elastic]
  • The average kinetic energy of these molecules is proportional to absolute temperature, meaning at any specific temperature they all have the same average kinetic energy

There are a few things to know about pressure too:

  • Pressure is caused by gas molecules colliding with container walls
  • This pressure correlates with how hard and what frequency they collide
  • This pressure of the impact is related to the speed x the mass of the molecules

So how does this tie into absolute temperature?

  • Where temperature doubles, kinetic energy of the molecules doubles
  • For all intents and purposes, two different gasses of the same temperature also have the same kinetic energy
  • The absolute temperature thus measures the average kinetic energy of molecules.
  • The lower average kinetic energy, the lower absolute temperature, and vice versa.

So what does this mean for molecular speed?

Obviously, while the theory states the average molecular speed, each individual molecule has its own speed- some fast and some slow. Where the temperature is higher, speed is higher.
Average kinetic energy is related to the root mean square of the speed [u]. Because mass never changes, speed must increase with temperature increases
E = ½ mu^2

So, how does this affect the gas laws?

We now knew that a constant temperature means the average kinetic energy will stay the same. We also now know this means that root mean square speed remains unaltered. This means the pressure will decrease per Boyle’s law, where volume increases but the temperature remains steady.
Where temperature remains steady but volume constant, we know that that increase in temperature will increase molecule speed. This will lead to more collisions, which in turn will boost momentum. This means an increase in pressure.
If we wish to maintain constant pressure, the volume will increase with increasing temperature per Charles’ law.
As you can see, the concept of kinetic molecular energy and the gas laws are critical to understanding. Study these laws carefully with the help of your physics tuition teacher, and you will be well on the way to acing your examination.

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