Water activity (\(a_w\)) is a measure of the availability of water in a substance for biological activity, and it is defined as the ratio of the vapour pressure of water in the substance to the vapour pressure of pure water at the same temperature.
- Option (1) refers to the vapour pressure of water in the substance but does not include the comparison to the vapour pressure of pure water, which is necessary for defining water activity.
- Option (2) includes the comparison to the vapour pressure of pure water, but at different temperatures, which is not the correct definition of water activity, as it must be measured at the same temperature.
- Option (3) is the correct definition, as water activity is the ratio of the vapour pressure of water in the substance to the vapour pressure of pure water at the same temperature.
- Option (4) just refers to the vapour pressure of pure water, which is not the complete definition of water activity.
Thus, the correct answer is option (3): a ratio of the vapour pressure of water in substance to vapour pressure of pure water at the same temperature.