If you double the volume of a sample of gas and then doubled the volume again without changing its pressure, how would this absolute temperature of the gas be affected

absolute temperature will increase fourfold

Increasing Volume while maintaining constant pressure requires a proportional increase in Temperature so the gas pressure will be maintained as constant.

Consider ...

V₁ = V₁ V₂ = 4V₁

T₁ = T₁ T₂ = ?

Charles Law = > T ∝ V at constant P ... that is, increasing temperature generates a proportional increase in volume to maintain constant pressure.

Empirical Charles Law Relation is ...

V₁/T₁ = V₂/T₂ = > T₂ = T₁ (V₂/V₁) = T₁ (4V₁/V₁) = 4T₁

Increasing Volume of a gas by 4 times requires a 4 times increase in absolute temperature in order to maintain constant pressure.