Important Equations

KE = Kinetic energy

m  =  Mass of each particle

v = Average velocity

k = Botzmann's constant

k1.3806503×10-23m2 kg s-2 K-1

T = Temperature

Diatomic Gases

Kinetic Energy and Diatomic Gases

      The expression for gas pressure developed from kinetic theory relates pressure and volume to the average molecular kinetic energy. Comparison with theideal gas law leads to an expression for temperature sometimes referred to as the kinetic temperature.

This leads to the expression

The more familiar form expresses the average molecular kinetic energy:

        It is important to note that the average kinetic energy used here is limited to the translational kinetic energy of the molecules. That is, they are treated as point masses and no account is made of internal degrees of freedom such as molecular rotation and vibration. This distinction becomes quite important when you deal with subjects like the specific heats of gases. When you try to assess specific heat, you must account for all the energy possessed by the molecules, and the temperature as ordinarily measured does not account for molecular rotation and vibration. The kinetic temperature is the variable needed for subjects like heat transfer, because it is the translational kinetic energy which leads to energy transfer from a hot area (larger kinetic temperature, higher molecular speeds) to a cold area (lower molecular speeds) in direct collisional transfer.

Definition Provided By Hyperphysics

Thermodynamic processes and the ideal gas law

Isobaric Process

    In an isobaric process is a thermodynamics in which the pressure in the chamber stays constant.  If the volume of the chamber is increased, then the temperature inside the chamber also has to increased.  As the temperature increases so does kinetic energy of the gas.  

    Think of it this way, imagine a chamber with only with only a couple of particles. These particles hit the sides of the chamber, and it is these collisions with the side of the chamber that gives us pressure.  If the volume is increased but the pressure stays the same, then that handful of particles have to hit the sides of the with the same rate, but now they have to move further to do it, so they need more kinetic energy to do it. 

    In an isobaric were the were the volume is decreased (when the chamber does work) the temperature would decrease, lowering the kinetic energy. 


Isochoric Process

    In an isochoric process the volume stays constant but the pressure is allowed to change. So in a system were the pressure is increased then the temperature has to increased.  The number of collisions with the surface of the container has to increased, so the amount of kinetic energy has to increase.  

    In an isochoric process were the pressure is decreased, then kinetic energy has been removed from the gas.  

Isothermal Process 

In an isothermal process the temperature in the container remains constant, allowing pressure and volume to change. If pressure increases then volume decreases at the exact amount, and vise verse.   When dealing with kinematic energy in a isothermal process it is important to understand if the temperature doesn't change then the kinetic energy doesn't change.