Now, Gay Lussac's law, also known as Amaton's law, says that pressure and temperature are directly proportional at constant moles n and volume v. As the temperature increases, our gas particles collide with the walls more rapidly. That's because they're absorbing the thermal energy and using it to propel themselves faster inside the container. This will cause an increase in my pressure. Remember, pressure itself equals force over the area. We said that the volume is constant, so your area would be constant; it's staying the same. If I'm increasing my temperature, my gas will move faster inside the container, they're going to hit the walls more rapidly but also with more force. So my force is increasing, my area is staying the same, causing my pressure to increase. This is why pressure and temperature are directly proportional. Remember that with all gas law calculations, we must use the SI units for temperature in Kelvin.
Now, what is the pressure-temperature relationship? They're directly proportional, so you just say that p is directly proportional to t, and that happens when moles and volume are fixed. To illustrate this, imagine two images of containers with movable pistons. In the first image, a heat source is not applied, so the temperature here would be low. The molecules don't have extra outside energy to absorb, so they're not moving as vigorously and rapidly. They're not hitting the container with as much force, and therefore our pressure would be low. But when I add a flame, the container absorbs the heat which eventually transitions to the molecules absorbing this heat, allowing them to move more rapidly and with greater force. So the temperature is high, which eventually leads to greater force, which leads to greater pressure. Pressure would be high. How would I depict this in a plot? They're both directly proportional so we'd say that they both would be increasing together so you'd have a line that's increasing over time.
What would their adjusted formula be or the Gay Lussac's formula? It would just be p1 / t1 = p2 / t2. Take a look at my ideal gas law applications section on how we could derive this formula. Remember, with these variables we'd say initial pressure is p1, initial temperature is t1, final pressure will be p2, and final temperature will be t2. Remember when discussing Gay Lussac's law or Amaton's law that pressure and temperature are directly proportional when our moles n and our volume v are constant or fixed.