Gay-Lussac's law states that an amount of gas at a constant mass and volume will have a pressure that varies proportionally with the absolute temperature. It is a direct mathematical relationship, and therefore when one value increases, the other will also increase.
This law is commonly used in applications such as the mechanism of pressure relief valves on gas cylinders. As the pressure of a cylinder builds due to increasing temperatures, the pressure will reach a certain point where the pressure relief valve will open in order to prevent an explosion.
Another common application is in the heating of aerosol cans such as deodorants and spray paint. When these cans are heated, the gas molecules have more energy and will collide with each other more frequently. This results in an increased pressure which is why there are warnings on these cans stating that they must be kept cool to avoid explosions.
The T1 and T2 relaxation times of a substance are related to the speed at which the molecular motions cause them to rotate. A substance with smaller molecules will have longer T1 and T2 relaxation times compared to a more dense, large molecule such as water or protein. This is why we have a wide range of MR imaging sequences such as echo-planar and spin-echo, all of which allow us to detect various structures in the body by measuring the T1 or T2 relaxation times. Currently, T2 mapping is the most popular technique for clinical MRI, and it can be used to visualize tissue contrast in several cardiac diseases including myocardial infarction, ischemic stroke, and perfusion MR imaging.