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. Determine the final temperature of the gas. Take = 1.5 .

Step-by-step solution

For an adiabatic process, the relation between temperature and volume is given by T₁ V₁^ - 1 = T₂ V₂^ - 1 Given T₁ = 300 K , V₁ = V , V₂ = V 2 , and = 1.5 . Substituting the values in the equation: 300 V^ 1.5 - 1 = T₂ ( V 2 )^ 1.5 - 1 300 V^ 0.5 = T₂ V^ 0.5 2^ 0.5 T₂ = 300 2 T₂ = 300 1.414 = 424.2 K The final temperature of the gas is approximately 424 K .