Dividing a rawΔ47[EG vs WG] byδ47[EG vs WG] we can get a slope just like the slope of the HGL?
Is it crrect to say that dividing a rawΔ47[EG vs WG] byδ47[EG vs WG], one probably can get a slope just like the slope of the heated gases line(HGL) and this slope can be used to correct the non-linearity effect ? Maybe it assume that the EG should be prepared at the temperature condition(maybe 25℃) where one store the working reference gas. Does this suggest that we don’t need to prepare a suite of gases that differ from one another in bulk composition in order to build the HGL?
To obtain the slope, you need as a minimum to devide the difference in Δ47[EG vs WG] by between two datapoints by the difference δ47[EG vs WG] between these two points. Ideally, these points need to be far apart in compositional space. The ratio of Δ47[EG vs WG] to δ47[EG vs WG] of a single point is meaningless. Also, note that you need the intercept of the line at δ47[EG vs WG]=0 axis to be able to correct for non-linearity.
You don't specifically need a heated gas, you could equilibrate your gas with water at any known temperature. As long as you know that these gases should all have the same Δ47[EG vs WG] value, it is possible to correct for non-linearity. However, the community has traditionally used heated gas because they are close to stochastic, and probably easier to produce and reproduce than equilibrated gases. You do need a range of composition though.
Now, if you don't want to bother about producing heated gases, you can always looks at doing a PBL correction. Plenty of papers out there explaining this approach.