Occupying 100 cc , an ideal gas is initially at a pressure of 2.5 10^5 Pa and a temperature of 300 K . It is adiabatically compressed to half its original volume. Evaluate the work done by the gas during this process. Take = 1.5 .

Step-by-step solution

Given: Initial volume V₁ = 100 cc = 10⁻⁴ m ^3 Initial pressure P₁ = 2.5 10^5 Pa Final volume V₂ = V₁ 2 = 50 cc = 0.5 10⁻⁴ m ^3 Ratio of specific heats = 1.5 For an adiabatic process, P₁ V₁^ = P₂ V₂^ P₂ = P₁ ( V₁ V₂ )^ P₂ = 2.5 10^5 (2)^ 1.5 = 2.5 10^5 2 2 = 5 2 10^5 Pa The work done by the gas in an adiabatic process is given by: W = P₁ V₁ - P₂ V₂ - 1 P₁ V₁ = (2.5 10^5) (10⁻⁴) = 25 J P₂ V₂ = (5 2 10^5) (0.5 10⁻⁴) = 2.5 2 10 = 25 2 J Substituting the values: W = 25 - 25 2 1.5 - 1 = 25(1 - 2 ) 0.5 W = 50(1 - 1.414) =