What is an Ideal Gas?

    An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly eleastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

Definition provided by Hyperphysics

The relationship between Temperature and Energy

     A lot of lay people mistakenly link temperature to energy.  Thou they maybe closely related they are not to same thing.  The temperature of a gase is related to the kinetic energy of the gas, or if you will, The Average Kinetic energy of each particle (molecule or atom).  This relationship is expressed in the Ideal Gas.  PV is a work equation, pressure = Force / Area, and volume is area times height.  So PV simplifies to Force x displacement or work. That means PV is the work done on or by the gas, adding or removing energy from the gas (and when energy is removed the temperature). 

      But why is it only kinetic energy? An ideal gas has particles that wont interact with other particle except in collisions.  So any electrostatic, gravitational, or magnetic energy is thrown (which for most situation it isn't ridiculous to do, with very same mass and charges, there should be very stored energy between particles, at lower temperatures it is a different story).  The only remaining potential energy that is of any concern nuclear, but because of the particles are not what we consider "high energy" meaning moving at incredibly high speed or not unstable we can ignore nuclear energy.

    Why average energy and not just energy.  Well think of what a gas is, a collection of particles that randomly move around colliding with each other exchanging momentum and energy.  So it is impossible for all of the energy to be divided up evenly and keep it that way.

Important Equations

k = Boltzmann constant

T = Temperature 

P = Pressure

V = Volume 

n = moles

= number of molecules

R = Gas Constant

V = Volume 

n = moles

= number of molecules

R = Gas Constant