A sample of nitrogen gas occupies a volume of `1.0 dm^(3)` at a pressure of `0.5` bar and at `40^(@)C`. Calculate the pressure the gas if compressed to `0.225 dm^(3)` at `-6^(@)C`.

Explanation

From the available data : `V_(1) = 1.0 dm^(3) , V_(2) = 0.225 dm^(3)`
`P_(1) = 0.5` bar , `P_(2) = ?`
`T_(1) = 40 + 273 = 313 K , T_(2) = -6 + 273 = 267 K`
According to Gas equation, `(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))` or `P_(2) = (P_(1)V_(1)T_(2))/(T_(1)V_(2))`
By substituting the values, `P_(2) = ((0.5 "bar") xx (1.0 dm^(3)) xx (267 K))/((313 K) xx (0.225 dm^(3))) = 1.896` bar