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 . Determine the number of moles of the gas in the sample.

Step-by-step solution

Using the ideal gas equation for the initial state: P₁ V₁ = n R T₁ Substituting the given values P₁ = 150 10^3 Pa , V₁ = 150 10⁻⁶ m ^3 , T₁ = 300 K , and R = 25 3 J/(mol K) : n = 150 10^3 150 10⁻⁶ 25 3 300 n = 22.5 2500 n = 0.009 moles