Heat transfer and thermal equilibrium | Thermodynamics | AP Chemistry | Khan Academy

Let's see. We have two samples of helium gas. One sample of helium gas is at temperature t1, and the other sample of helium gas is at temperature t2. If t2 is greater than t1, that means, on average, the particles of helium gas in the second box are moving faster than the particles of helium gas in the first box. We can tell the particles in the second box are moving faster because, on average, the length of these arrows indicating the velocity vector in the box on the right are longer than the length of the arrows in the first box.

The equation for kinetic energy is equal to one half mv squared, where m is the mass of a particle and v is the velocity of a particle. Since the gas particles in the box on the right are, on average, traveling faster and have higher velocities, the average kinetic energy of the particles in the box on the right is higher than the average kinetic energy for the particles in the box on the left. Thus, the average kinetic energy is proportional to the temperature. The higher the temperature, the higher the average kinetic energy of the particles.

Instead of gases, let's look at two metal blocks made of the same material. One of the metal blocks is at temperature t1, and the other metal block is at temperature t2. Let's say the temperature t2 is greater than t1. What that means is the particles in the metal box on the right are, on average, moving faster than the particles in the metal box on the left. That means that the average kinetic energy of the particles in the box on the right is greater than the average kinetic energy of the particles in the box on the left.

Also, notice right now our two pieces of metal are not touching each other, so there's a little bit of space between them. Next, we bring the two objects and we put them in contact with each other. Now, there are collisions between the particles that touch, and this results in the transfer of energy from the hotter object to the cooler object. So, heat flows from the object at the higher temperature to the object at the lower temperature.

The hot atoms in the metal object on the right start to move a little bit slower, whereas the colder atoms in the metal on the left start to move a little bit faster. The transfer of energy continues until both objects have the same final temperature, and we say that thermal equilibrium has been reached.

So, here we have our two objects, and the two objects are at the same final temperature, which means we have reached thermal equilibrium. Since we've reached thermal equilibrium, there's no more flow of heat between the two objects. Since both objects are at the same final temperature, that means the average kinetic energy of the particles in both objects is now the same.