# How to 'normalise' the effect of temperature on pressure to determine an accurate leak rate

I want to determine the leak rate of a container. I pumped it with air and measured the temperature and pressure within the container. What I observed is that, due to fluctuations of temperature in the room, the pressure rose and fell with it. The pressure was also steadily falling due to leaks. I'm wondering if there is a data analytical way that is fair to 'normalise' the temperature and pressure such that I can accurately determine the leak rate of my container. i.e. how to ignore the effect of temperature on pressure in the analysis.

Thanks

As a first approximation, you could use ideal gas law, which you can easily transform to a volume as a function od temperature to pressure ratio:

$$V\left(\frac{T}{p}\right) = n\cdot R\cdot \frac{T}{p}$$

In your case $$n\cdot R$$ should be constant, so you can determine it from the first (few) measurement(s).

The Nondestructive Testing handbook (vol 2, Leak Testing) published by ASNT, and various other sources, have equations for this. But they are ultimately based on ideal gas law. The mass change over a time period $$\Delta t$$ for a constant volume container is:

$$\frac {m_1-m_2}{\Delta t} = \frac{V}{\Delta t} \left[\frac {P_1}{T_1} - \frac{P_2}{T_2}\right]$$

Where the quantity on the left is the average leak rate (kg/s) over the time period.

There are also ways of doing a best fit regression line of the $$P$$ vs time or $$P/T$$ vs time, given a set of data points.