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 pressure to its initial pressure.

Step-by-step solution

For an adiabatic process, the equation of state is given by: P₁ V₁^ = P₂ V₂^ Rearranging for the ratio of final pressure to initial pressure: P₂ P₁ = ( V₁ V₂ )^ Substituting the given values V₁ = 4.00 L, V₂ = 3.00 L, and = 1.5 = 3 2 : P₂ P₁ = ( 4 3 )^ 3/2 P₂ P₁ = 4^ 3/2 3^ 3/2 = 8 3 3 Using 3 1.732 : P₂ P₁ = 8 3 1.732 = 8 5.196 1.54