If a gas is compressed to half of its original volume at 27°C, to what temperature should it be heated to make it occupy its original volume ?

Use Charles's law (volume ∝ absolute temperature at constant pressure): V1/T1 = V2/T2. The gas at 27°C has T1 = 27 + 273 = 300 K . After compression its volume is V1' = V/2 at the same temperature 300 K. To restore the original volume V (i.e. V2 = V) we need V2/V1' = T2/T1 = 2, so T2 = 2 × 300 K = 600 K. Converting back to Celsius gives 600 − 273 = 327°C. Thus the gas must be heated to 327°C to occupy its original volume [1].

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 22: Vertical Distribution of Temperature > Example 2: Vehicle tube > p. 296