If a room temperature piece of metal, let's say a penny, is placed into a room temperature glass of water, the temperature of both objects stays the same. This might not seem revolutionary, but an exploration into the particulate details of why this is can provide great insight into understanding why temperature is critical to discussing chemicals. In the example given, we have copper particles (we will assume it is an old penny) that are more massive than the water particles. When mixed these particles will collide with each other. If the temperature of both remains the same that means that the motion of neither set of particles is increasing or decreasing. That is interesting because the copper particles are more massive than the water particles.
During a collision, the force on both particles involved in the collision must be the same. If one particle of greater mass collides with a particle of smaller mass, the force on both is the same. Since the masses are different this means that the accelerations will not be the same. So in our copper and water example we have particles colliding without changing speed despite the fact that they have different accelerations during each collision. This can only be true is the particles on average are moving at different speeds. At the same temperature, copper particles move slower than water particles. When the collision occurs, the slower moving copper particles require less acceleration to maintain the same speed in a different direction. The faster moving water particles require more acceleration to maintain the same speed in a different direction. So there is some breaking even point, where faster and less massive particles will not change speed over time when in contact with slower and more massive particles. This is in spite of frequent collisions. Where does this break even point occur? For elastic collisions (no vibrations, rotations, etc.) we get this ratio between particles speeds and particle masses using simple shortcuts like conservation of momentum and conservation of energy (true for elastic collisions for the system of particles). This break even point is when the less massive particles on average move slower by the square root of the ratio of the masses. v1 = v2 * √(m2/m1)
This relationship is often derived from setting the kinetic energies of the two particles equal to each other. We can see the same results from this analysis. In order for ½ m1v12 = ½ m2v22 the more massive particles require a smaller velocity. If the velocities were the same, the collisions that resulted would cause the smaller particles to increase in velocity and the more massive particles to decrease in velocity until they reached a thermal equilibrium. When they reached this point, there temperatures would be equal. The purpose of temperature then is to give an equivalence of motion combining mass and speed that shows whether different mass particles will change motion when in contact. When temperatures do not match, speeds will change and we refer to this transfer of motion as heat. For an individual substance, temperature is related to motion or energy. As motion or energy increases, so does temperature. For the Kelvin scale they are even directly proportional. But the simplification of when heat will occur is such an important result of temperature that it deserves mention.
For simplification reasons, the variance beyond average speed is ignored for most of this discussion.
