The mathematical relationship between a change in temperature and the resulting change in pressure in an ideal gas is given by the ideal gas law, which is expressed as:
\(PV = nRT\)
Where:
- \(P\) represents pressure.
- \(V\) represents volume.
- \(n\) represents the number of moles of gas.
- \(R\) is the gas constant.
- \(T\) represents temperature (in Kelvin).
Specifically, if you want to understand the relationship between a change in temperature (\(ΔT\)) and the resulting change in pressure (\(ΔP\)) while keeping other factors constant, you can use the following form of the ideal gas law:
\(ΔP = (nR/ V) ΔT\)
This equation shows that, in an ideal gas, an increase in temperature (\(ΔT\)) will lead to an increase in pressure (\(ΔP\)) if other factors are held constant.