An ideal gas possessing = 1.5 is initially at 300 K with a volume of 1 litre. It is suddenly compressed to half its original volume. Determine the final temperature of the gas.

Step-by-step solution

For an adiabatic process, the relation between temperature and volume is T₁ V₁^ - 1 = T₂ V₂^ - 1 . Rearranging for the final temperature gives T₂ = T₁ ( V₁ V₂ )^ - 1 . Substituting the given values T₁ = 300 K , V₁ V₂ = 2 , and = 1.5 : T₂ = 300 (2)^ 1.5 - 1 = 300 2^ 0.5 = 300 2 K . Using 2 1.414 , the final temperature is 300 1.414 = 424.2 K .