An ideal gas ( = 1.5 ) occupying 1 litre at 300 K and an initial pressure of 100 kPa undergoes a sudden compression to half its original volume. Calculate the work done by the gas during this process.

Step-by-step solution

The work done by the gas in an adiabatic process is given by W = P₁ V₁ - P₂ V₂ - 1 . The initial state is P₁ = 10^5 Pa and V₁ = 10⁻³ m ^3 , so P₁ V₁ = 100 J . The final volume is V₂ = 0.5 10⁻³ m ^3 and the final pressure is P₂ = 2 2 10^5 Pa . The product P₂ V₂ = (2 2 10^5) (0.5 10⁻³) = 100 2 141.4 J . Substituting these into the work equation gives W = 100 - 141.4 1.5 - 1 = -41.4 0.5 = -82.8 J .