To solve this problem, we can use the combined gas law, which combines Boyle's Law, Charles's Law, and Gay-Lussac's Law. The combined gas law is expressed as:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where: P₁ = initial pressure V₁ = initial volume T₁ = initial temperature (in Kelvin) P₂ = final pressure (what we want to find) V₂ = final volume (half the initial volume) T₂ = final temperature (in Kelvin)
Let's solve the problem step by step:
Step 1: Convert temperatures to Kelvin T₁ = 27°C + 273.15 = 300.15 K T₂ = 127°C + 273.15 = 400.15 K
Step 2: Substitute the given values into the combined gas law (P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
(3 atm * 4 m³) / (300.15 K) = (P₂ * 2 m³) / (400.15 K)
Step 3: Solve for P₂ P₂ = [(3 atm * 4 m³) / (300.15 K)] * (400.15 K / 2 m³) P₂ = 7.99 atm (rounded to two decimal places)
Therefore, if the trapped air is compressed into half the volume and heated to 127°C, the pressure will be approximately 7.99 atm.