What is the relationship between temperature and pressure?
Temperature and pressure of a gas are directly proportional to each other. This can be also be written as:
`P alpha T`
This also means that
`P/T = constant`
`P_1/T_1 = P_2/T_2`
where P1 and P2 are pressures at temperatures T1 and T2, respectively.
This is true if the volume is held constant.
One way to think about the pressure-temperature relationship is to consider what happens when the temperature changes. If we increase the temperature of a gas, its molecules will have more kinetic energy and they will have more collisions with each other and the container they are held in (as long as the container volume is fixed). This will cause an increase in the pressure in the container. On the other hand, if we decrease the gas temperature, the molecules will have lesser kinetic energy and this will result in a reduced number of collisions with the container and hence lower pressure.
The above equation is also known as Gay-Lussac's Law and can be derived from the ideal gas law.
Hope this helps.