An ideal gas ( = 1.5 ) undergoes an adiabatic change in volume from 4.00 litres to 3.00 litres. Determine the ratio of its final temperature to its initial temperature.

Step-by-step solution

For an adiabatic process, the relation between temperature and volume is given by: T V^ - 1 = constant Therefore, T₁ V₁^ - 1 = T₂ V₂^ - 1 Rearranging for the ratio of final to initial temperature: T₂ T₁ = ( V₁ V₂ )^ - 1 Substituting the given values V₁ = 4.00 L, V₂ = 3.00 L, and = 1.5 : T₂ T₁ = ( 4.00 3.00 )^ 1.5 - 1 T₂ T₁ = ( 4 3 )^ 0.5 T₂ T₁ = 4 3 = 2 3 Using 3 1.732 : T₂ T₁ = 2 1.732 1.15