An ideal gas sample ( = 1.5 ) is adiabatically compressed from a volume of 150 cm ^3 to 50 cm ^3 . The initial pressure and initial temperature are 150 kPa and 300 K . Calculate the final pressure and final temperature of the gas.

Step-by-step solution

For an adiabatic process, the relation between pressure and volume is given by P₁ V₁^ = P₂ V₂^ . Substituting the given values: P₂ = P₁ ( V₁ V₂ )^ P₂ = 150 ( 150 50 )^ 1.5 P₂ = 150 3^ 1.5 = 150 3 3 = 450 1.732 780 kPa The relation between temperature and volume for an adiabatic process is T₁ V₁^ - 1 = T₂ V₂^ - 1 . T₂ = T₁ ( V₁ V₂ )^ - 1 T₂ = 300 ( 150 50 )^ 1.5 - 1 T₂ = 300 3^ 0.5 = 300 3 = 300 1.732 520 K